library(tidyverse)
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## ✔ ggplot2 3.4.3 ✔ tibble 3.2.1
## ✔ lubridate 1.9.2 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
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library(tidymodels)
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## ✔ recipes 1.0.8
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library(ggforce)
library(mctest)
library(olsrr)
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library(jtools)
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library(ggcorrplot)
library(yardstick)
library(car)
## Loading required package: carData
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## Attaching package: 'car'
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library(moments)
library(GGally)
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library(psych)
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library(fastDummies)
## Thank you for using fastDummies!
## To acknowledge our work, please cite the package:
## Kaplan, J. & Schlegel, B. (2023). fastDummies: Fast Creation of Dummy (Binary) Columns and Rows from Categorical Variables. Version 1.7.1. URL: https://github.com/jacobkap/fastDummies, https://jacobkap.github.io/fastDummies/.
NHL <- read_csv("train.csv") %>% as_tibble()
## New names:
## Rows: 612 Columns: 154
## ── Column specification
## ──────────────────────────────────────────────────────── Delimiter: "," chr
## (10): Born, City, Pr/St, Cntry, Nat, Hand, Last Name, First Name, Posit... dbl
## (144): Salary, Ht, Wt, DftYr, DftRd, Ovrl, GP, G, A, A1, A2, PTS, PM, E+...
## ℹ Use `spec()` to retrieve the full column specification for this data. ℹ
## Specify the column types or set `show_col_types = FALSE` to quiet this message.
## • `TOI/GP` -> `TOI/GP...29`
## • `TOI/GP` -> `TOI/GP...30`
## • `iCF` -> `iCF...41`
## • `iCF` -> `iCF...42`
## • `iSF` -> `iSF...44`
## • `iSF` -> `iSF...45`
## • `iSF` -> `iSF...46`
## • `sDist` -> `sDist...52`
## • `sDist` -> `sDist...53`
## • `iHF` -> `iHF...55`
## • `iHF` -> `iHF...56`
## • `iGVA` -> `iGVA...60`
## • `iTKA` -> `iTKA...61`
## • `iBLK` -> `iBLK...62`
## • `iGVA` -> `iGVA...63`
## • `iTKA` -> `iTKA...64`
## • `iBLK` -> `iBLK...65`
## • `iFOW` -> `iFOW...67`
## • `iFOL` -> `iFOL...68`
## • `iFOW` -> `iFOW...69`
## • `iFOL` -> `iFOL...70`
NHL <- na.omit(NHL)
summary(NHL)
## Salary Born City Pr/St
## Min. : 575000 Length:359 Length:359 Length:359
## 1st Qu.: 750000 Class :character Class :character Class :character
## Median : 950000 Mode :character Mode :character Mode :character
## Mean : 2456544
## 3rd Qu.: 3750000
## Max. :13800000
## Cntry Nat Ht Wt
## Length:359 Length:359 Min. :67.00 Min. :160
## Class :character Class :character 1st Qu.:72.00 1st Qu.:191
## Mode :character Mode :character Median :73.00 Median :202
## Mean :73.06 Mean :202
## 3rd Qu.:74.50 3rd Qu.:212
## Max. :78.00 Max. :244
## DftYr DftRd Ovrl Hand
## Min. :1997 Min. :1.000 Min. : 1.00 Length:359
## 1st Qu.:2006 1st Qu.:1.000 1st Qu.: 18.00 Class :character
## Median :2009 Median :2.000 Median : 51.00 Mode :character
## Mean :2009 Mean :2.811 Mean : 69.91
## 3rd Qu.:2012 3rd Qu.:4.000 3rd Qu.:110.00
## Max. :2016 Max. :9.000 Max. :279.00
## Last Name First Name Position Team
## Length:359 Length:359 Length:359 Length:359
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
## GP G A A1
## Min. : 1.00 Min. : 0.000 Min. : 0.00 Min. : 0.000
## 1st Qu.:26.50 1st Qu.: 1.000 1st Qu.: 2.00 1st Qu.: 1.000
## Median :65.00 Median : 5.000 Median :11.00 Median : 5.000
## Mean :53.42 Mean : 7.947 Mean :13.35 Mean : 7.362
## 3rd Qu.:79.00 3rd Qu.:12.500 3rd Qu.:21.00 3rd Qu.:11.000
## Max. :82.00 Max. :44.000 Max. :55.00 Max. :36.000
## A2 PTS PM E+/-
## Min. : 0.000 Min. : 0.00 Min. :-31.0000 Min. :-19.00000
## 1st Qu.: 1.000 1st Qu.: 4.00 1st Qu.: -6.0000 1st Qu.: -3.20000
## Median : 5.000 Median :16.00 Median : -1.0000 Median : -0.40000
## Mean : 5.986 Mean :21.29 Mean : -0.4401 Mean : -0.05822
## 3rd Qu.: 9.000 3rd Qu.:35.00 3rd Qu.: 5.0000 3rd Qu.: 2.45000
## Max. :28.000 Max. :89.00 Max. : 34.0000 Max. : 20.30000
## PIM Shifts TOI TOIX
## Min. : 0.00 Min. : 13.0 Min. : 429 Min. : 7.2
## 1st Qu.: 10.00 1st Qu.: 460.5 1st Qu.: 20374 1st Qu.: 339.4
## Median : 24.00 Median :1330.0 Median : 57408 Median : 952.4
## Mean : 28.57 Mean :1171.1 Mean : 53497 Mean : 887.5
## 3rd Qu.: 38.00 3rd Qu.:1798.0 3rd Qu.: 83899 3rd Qu.:1387.2
## Max. :154.00 Max. :2657.0 Max. :133550 Max. :2218.9
## TOI/GP...29 TOI/GP...30 TOI% IPP%
## Min. : 6.75 Min. : 6.75 Min. :13.10 Min. : 0.00
## 1st Qu.:12.25 1st Qu.:12.19 1st Qu.:22.90 1st Qu.: 34.60
## Median :15.42 Median :15.41 Median :27.40 Median : 54.80
## Mean :15.42 Mean :15.40 Mean :27.57 Mean : 49.92
## 3rd Qu.:18.43 3rd Qu.:18.43 3rd Qu.:32.30 3rd Qu.: 67.60
## Max. :27.15 Max. :27.12 Max. :44.90 Max. :100.00
## SH% SV% PDO F/60
## Min. : 0.000 Min. :0.6670 Min. : 750.0 Min. : 0.000
## 1st Qu.: 6.300 1st Qu.:0.9040 1st Qu.: 978.0 1st Qu.: 1.685
## Median : 8.000 Median :0.9160 Median : 997.0 Median : 2.270
## Mean : 7.723 Mean :0.9151 Mean : 992.3 Mean : 2.270
## 3rd Qu.: 9.600 3rd Qu.:0.9270 3rd Qu.:1016.0 3rd Qu.: 2.980
## Max. :40.000 Max. :1.0000 Max. :1257.0 Max. :10.780
## A/60 Pct% Diff Diff/60
## Min. : 0.000 Min. : 0.00 Min. :-44.000 Min. :-16.740
## 1st Qu.: 2.075 1st Qu.: 39.10 1st Qu.: -7.000 1st Qu.: -0.930
## Median : 2.470 Median : 48.60 Median : -1.000 Median : -0.090
## Mean : 2.535 Mean : 45.92 Mean : 1.774 Mean : -0.265
## 3rd Qu.: 2.865 3rd Qu.: 56.75 3rd Qu.: 10.000 3rd Qu.: 0.650
## Max. :16.740 Max. :100.00 Max. : 61.000 Max. : 5.390
## iCF...41 iCF...42 iFF iSF...44
## Min. : 1.0 Min. : 1.0 Min. : 1.0 Min. : 0.00
## 1st Qu.: 50.5 1st Qu.: 51.5 1st Qu.: 38.5 1st Qu.: 26.00
## Median :156.0 Median :156.0 Median :116.0 Median : 82.00
## Mean :166.3 Mean :166.4 Mean :124.6 Mean : 89.91
## 3rd Qu.:253.0 3rd Qu.:253.0 3rd Qu.:188.5 3rd Qu.:137.50
## Max. :509.0 Max. :508.0 Max. :404.0 Max. :303.00
## iSF...45 iSF...46 ixG iSCF
## Min. : 0.00 Min. : 0.00 Min. : 0.000 Min. : 0.00
## 1st Qu.: 26.00 1st Qu.: 26.00 1st Qu.: 1.900 1st Qu.: 3.50
## Median : 82.00 Median : 82.00 Median : 5.900 Median : 13.00
## Mean : 90.12 Mean : 90.14 Mean : 8.025 Mean : 26.57
## 3rd Qu.:138.00 3rd Qu.:138.00 3rd Qu.:12.100 3rd Qu.: 46.00
## Max. :302.00 Max. :302.00 Max. :33.000 Max. :139.00
## iRB iRS iDS sDist...52
## Min. : 0.000 Min. : 0.000 Min. : 0.00 Min. : 0.00
## 1st Qu.: 1.000 1st Qu.: 2.000 1st Qu.: 4.00 1st Qu.:27.10
## Median : 4.000 Median : 6.000 Median :11.00 Median :31.60
## Mean : 6.396 Mean : 7.735 Mean :14.13 Mean :36.08
## 3rd Qu.:10.000 3rd Qu.:12.000 3rd Qu.:21.00 3rd Qu.:47.80
## Max. :41.000 Max. :32.000 Max. :63.00 Max. :77.50
## sDist...53 Pass iHF...55 iHF...56
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.:25.20 1st Qu.: 37.85 1st Qu.: 25.00 1st Qu.: 25.00
## Median :29.10 Median :118.80 Median : 59.00 Median : 58.00
## Mean :33.40 Mean :142.28 Mean : 69.42 Mean : 69.25
## 3rd Qu.:44.55 3rd Qu.:224.00 3rd Qu.: 94.00 3rd Qu.: 94.00
## Max. :65.50 Max. :501.20 Max. :364.00 Max. :364.00
## iHA iHDf iMiss iGVA...60
## Min. : 0.00 Min. :-114.000 Min. : 0.0 Min. : 0.00
## 1st Qu.: 26.50 1st Qu.: -17.000 1st Qu.: 12.0 1st Qu.: 6.50
## Median : 62.00 Median : 1.000 Median : 33.0 Median : 22.00
## Mean : 62.97 Mean : 6.279 Mean : 34.8 Mean : 24.99
## 3rd Qu.: 90.00 3rd Qu.: 22.500 3rd Qu.: 54.0 3rd Qu.: 39.00
## Max. :215.00 Max. : 227.000 Max. :109.0 Max. :102.00
## iTKA...61 iBLK...62 iGVA...63 iTKA...64
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.0
## 1st Qu.: 4.00 1st Qu.: 12.00 1st Qu.: 6.50 1st Qu.: 4.0
## Median :16.00 Median : 29.00 Median : 22.00 Median :16.0
## Mean :19.56 Mean : 44.34 Mean : 24.91 Mean :19.5
## 3rd Qu.:30.00 3rd Qu.: 61.50 3rd Qu.: 39.00 3rd Qu.:30.0
## Max. :96.00 Max. :213.00 Max. :102.00 Max. :96.0
## iBLK...65 BLK% iFOW...67 iFOL...68
## Min. : 0.00 Min. : 0.000 Min. : 0.00 Min. : 0.00
## 1st Qu.: 12.00 1st Qu.: 2.900 1st Qu.: 0.00 1st Qu.: 0.00
## Median : 29.00 Median : 4.400 Median : 2.00 Median : 2.00
## Mean : 44.25 Mean : 5.134 Mean : 86.65 Mean : 86.29
## 3rd Qu.: 61.50 3rd Qu.: 7.200 3rd Qu.: 42.00 3rd Qu.: 47.50
## Max. :213.00 Max. :16.700 Max. :1089.00 Max. :906.00
## iFOW...69 iFOL...70 FO% %FOT
## Min. : 0.00 Min. : 0.00 Min. : 0.0 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.0 1st Qu.: 0.00
## Median : 2.00 Median : 2.00 Median : 33.3 Median : 0.90
## Mean : 86.46 Mean : 86.08 Mean : 29.2 Mean :19.31
## 3rd Qu.: 42.00 3rd Qu.: 47.50 3rd Qu.: 50.0 3rd Qu.:25.60
## Max. :1083.00 Max. :906.00 Max. :100.0 Max. :99.20
## dzFOW dzFOL nzFOW nzFOL
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00
## Median : 0.00 Median : 0.00 Median : 0.00 Median : 0.00
## Mean : 28.69 Mean : 29.02 Mean : 27.58 Mean : 27.75
## 3rd Qu.: 8.00 3rd Qu.: 11.00 3rd Qu.: 12.00 3rd Qu.: 13.00
## Max. :429.00 Max. :344.00 Max. :324.00 Max. :326.00
## ozFOW ozFOL FOW.Up FOL.Up
## Min. : 0.00 Min. : 0.00 Min. : 0.0 Min. : 0.0
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.0 1st Qu.: 0.0
## Median : 1.00 Median : 1.00 Median : 0.0 Median : 0.0
## Mean : 30.36 Mean : 29.49 Mean : 26.4 Mean : 25.6
## 3rd Qu.: 17.00 3rd Qu.: 19.00 3rd Qu.: 13.0 3rd Qu.: 14.0
## Max. :420.00 Max. :390.00 Max. :385.0 Max. :287.0
## FOW.Down FOL.Down FOW.Close FOL.Close
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00
## Median : 1.00 Median : 1.00 Median : 1.00 Median : 2.00
## Mean : 28.86 Mean : 29.32 Mean : 53.86 Mean : 53.52
## 3rd Qu.: 13.50 3rd Qu.: 17.00 3rd Qu.: 27.00 3rd Qu.: 30.00
## Max. :329.00 Max. :302.00 Max. :679.00 Max. :549.00
## OTG 1G GWG ENG
## Min. :0.0000 Min. : 0.000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.: 0.000 1st Qu.:0.000 1st Qu.:0.0000
## Median :0.0000 Median : 1.000 Median :1.000 Median :0.0000
## Mean :0.2201 Mean : 1.501 Mean :1.326 Mean :0.3649
## 3rd Qu.:0.0000 3rd Qu.: 2.000 3rd Qu.:2.000 3rd Qu.:0.0000
## Max. :5.0000 Max. :12.000 Max. :9.000 Max. :4.0000
## PSG PSA G.Bkhd G.Dflct
## Min. :0.00000 Min. :0.00000 Min. : 0.0000 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.: 0.0000 1st Qu.:0.0000
## Median :0.00000 Median :0.00000 Median : 0.0000 Median :0.0000
## Mean :0.01393 Mean :0.05571 Mean : 0.7409 Mean :0.2312
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.: 1.0000 3rd Qu.:0.0000
## Max. :1.00000 Max. :1.00000 Max. :10.0000 Max. :3.0000
## G.Slap G.Snap G.Tip G.Wrap
## Min. : 0.0000 Min. : 0.000 Min. :0.0000 Min. :0.00000
## 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.:0.0000 1st Qu.:0.00000
## Median : 0.0000 Median : 0.000 Median :0.0000 Median :0.00000
## Mean : 0.9359 Mean : 1.284 Mean :0.8496 Mean :0.08635
## 3rd Qu.: 1.0000 3rd Qu.: 2.000 3rd Qu.:1.0000 3rd Qu.:0.00000
## Max. :12.0000 Max. :13.000 Max. :9.0000 Max. :2.00000
## G.Wrst CBar Post Over
## Min. : 0.000 Min. :0.0000 Min. :0.000 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.: 1.000
## Median : 2.000 Median :0.0000 Median :1.000 Median : 3.000
## Mean : 3.808 Mean :0.3287 Mean :1.457 Mean : 3.437
## 3rd Qu.: 6.000 3rd Qu.:1.0000 3rd Qu.:2.000 3rd Qu.: 5.000
## Max. :21.000 Max. :6.0000 Max. :8.000 Max. :18.000
## Wide S.Bkhd S.Dflct S.Slap
## Min. : 0.00 Min. : 0.000 Min. : 0.000 Min. : 0.00
## 1st Qu.:10.00 1st Qu.: 1.000 1st Qu.: 0.000 1st Qu.: 2.00
## Median :27.00 Median : 5.000 Median : 0.000 Median : 8.00
## Mean :29.58 Mean : 7.284 Mean : 1.231 Mean : 16.18
## 3rd Qu.:45.50 3rd Qu.:12.000 3rd Qu.: 2.000 3rd Qu.: 21.50
## Max. :98.00 Max. :44.000 Max. :18.000 Max. :141.00
## S.Snap S.Tip S.Wrap S.Wrst
## Min. : 0.0 Min. : 0.000 Min. :0.0000 Min. : 0.00
## 1st Qu.: 3.0 1st Qu.: 0.000 1st Qu.:0.0000 1st Qu.: 12.50
## Median :10.0 Median : 2.000 Median :0.0000 Median : 41.00
## Mean :14.2 Mean : 4.454 Mean :0.9638 Mean : 45.81
## 3rd Qu.:20.0 3rd Qu.: 7.000 3rd Qu.:1.0000 3rd Qu.: 69.00
## Max. :77.0 Max. :41.000 Max. :9.0000 Max. :182.00
## iPenT iPenD iPENT iPEND
## Min. : 0.00 Min. : 0.000 Min. : 0.00 Min. : 0.000
## 1st Qu.: 4.00 1st Qu.: 2.000 1st Qu.: 4.00 1st Qu.: 2.000
## Median :10.00 Median : 7.000 Median :10.00 Median : 6.000
## Mean :11.49 Mean : 9.287 Mean :10.93 Mean : 7.919
## 3rd Qu.:16.00 3rd Qu.:14.000 3rd Qu.:16.00 3rd Qu.:12.000
## Max. :48.00 Max. :47.000 Max. :44.00 Max. :35.000
## iPenDf NPD Min Maj
## Min. :-28.000 Min. :-19.400 Min. : 0.00 Min. : 0.000
## 1st Qu.: -6.000 1st Qu.: -3.200 1st Qu.: 4.00 1st Qu.: 0.000
## Median : -1.000 Median : 0.000 Median : 9.00 Median : 0.000
## Mean : -2.201 Mean : -0.322 Mean :10.12 Mean : 1.114
## 3rd Qu.: 1.000 3rd Qu.: 3.000 3rd Qu.:15.00 3rd Qu.: 1.000
## Max. : 20.000 Max. : 19.400 Max. :39.00 Max. :14.000
## Match Misc Game CF
## Min. :0.000000 Min. :0.0000 Min. :0.00000 Min. : 8.0
## 1st Qu.:0.000000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.: 287.5
## Median :0.000000 Median :0.0000 Median :0.00000 Median : 813.0
## Mean :0.005571 Mean :0.1727 Mean :0.07242 Mean : 825.9
## 3rd Qu.:0.000000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:1283.0
## Max. :1.000000 Max. :4.0000 Max. :2.00000 Max. :2308.0
## CA FF FA SF
## Min. : 6.0 Min. : 5.0 Min. : 5.0 Min. : 4.0
## 1st Qu.: 306.0 1st Qu.: 203.0 1st Qu.: 228.5 1st Qu.: 146.0
## Median : 863.0 Median : 603.0 Median : 645.0 Median : 441.0
## Mean : 812.9 Mean : 615.6 Mean : 604.7 Mean : 443.5
## 3rd Qu.:1226.0 3rd Qu.: 957.5 3rd Qu.: 922.5 3rd Qu.: 692.5
## Max. :2009.0 Max. :1668.0 Max. :1510.0 Max. :1181.0
## SA xGF xGA SCF
## Min. : 2.0 Min. : 0.20 Min. : 0.40 Min. : 0.0
## 1st Qu.: 162.0 1st Qu.: 12.25 1st Qu.:13.80 1st Qu.: 39.0
## Median : 469.0 Median : 37.90 Median :40.10 Median :124.0
## Mean : 434.4 Mean : 39.66 Mean :38.58 Mean :131.7
## 3rd Qu.: 667.5 3rd Qu.: 62.15 3rd Qu.:58.75 3rd Qu.:206.0
## Max. :1073.0 Max. :111.10 Max. :97.20 Max. :419.0
## SCA GF GA RBF
## Min. : 0.0 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 46.0 1st Qu.: 10.00 1st Qu.: 12.00 1st Qu.: 10.00
## Median :131.0 Median : 35.00 Median : 39.00 Median : 28.00
## Mean :128.4 Mean : 38.74 Mean : 36.97 Mean : 31.77
## 3rd Qu.:197.5 3rd Qu.: 64.50 3rd Qu.: 56.50 3rd Qu.: 48.00
## Max. :344.0 Max. :120.00 Max. :100.00 Max. :110.00
## RBA RSF RSA DSF
## Min. : 0.00 Min. : 0.0 Min. : 0.00 Min. : 0.00
## 1st Qu.:11.00 1st Qu.: 12.0 1st Qu.: 14.50 1st Qu.: 23.00
## Median :29.00 Median : 37.0 Median : 39.00 Median : 68.00
## Mean :29.91 Mean : 38.9 Mean : 38.58 Mean : 70.67
## 3rd Qu.:44.50 3rd Qu.: 59.0 3rd Qu.: 57.00 3rd Qu.:107.00
## Max. :95.00 Max. :130.0 Max. :112.00 Max. :213.00
## DSA FOW FOL HF
## Min. : 0.00 Min. : 4.0 Min. : 4.0 Min. : 0.0
## 1st Qu.: 26.50 1st Qu.: 142.5 1st Qu.: 152.5 1st Qu.:156.0
## Median : 73.00 Median : 442.0 Median : 460.0 Median :350.0
## Mean : 68.49 Mean : 437.8 Mean : 434.6 Mean :329.5
## 3rd Qu.:102.00 3rd Qu.: 678.5 3rd Qu.: 667.5 3rd Qu.:477.5
## Max. :185.00 Max. :1257.0 Max. :1196.0 Max. :926.0
## HA GVA TKA PENT
## Min. : 2.0 Min. : 0.0 Min. : 0.00 Min. : 0.00
## 1st Qu.:153.0 1st Qu.: 44.0 1st Qu.: 32.00 1st Qu.: 21.00
## Median :336.0 Median :126.0 Median : 93.00 Median : 55.00
## Mean :318.8 Mean :130.5 Mean : 97.39 Mean : 50.93
## 3rd Qu.:468.0 3rd Qu.:201.5 3rd Qu.:147.00 3rd Qu.: 76.00
## Max. :870.0 Max. :388.0 Max. :347.00 Max. :122.00
## PEND OPS DPS PS
## Min. : 0.00 Min. :-1.500 Min. :-0.200 Min. :-1.200
## 1st Qu.: 20.50 1st Qu.:-0.100 1st Qu.: 0.300 1st Qu.: 0.300
## Median : 53.00 Median : 0.500 Median : 1.100 Median : 2.000
## Mean : 50.01 Mean : 1.334 Mean : 1.402 Mean : 2.741
## 3rd Qu.: 75.00 3rd Qu.: 2.300 3rd Qu.: 2.000 3rd Qu.: 4.600
## Max. :127.00 Max. :10.500 Max. : 7.200 Max. :12.600
## OTOI Grit DAP Pace
## Min. : 33.51 Min. : 1.0 Min. : 0.000 Min. : 77.6
## 1st Qu.:1035.25 1st Qu.: 59.5 1st Qu.: 5.300 1st Qu.:104.8
## Median :2604.66 Median :132.0 Median : 7.800 Median :109.1
## Mean :2116.05 Mean :143.4 Mean : 9.516 Mean :109.1
## 3rd Qu.:3057.62 3rd Qu.:208.0 3rd Qu.:12.200 3rd Qu.:114.2
## Max. :3521.78 Max. :622.0 Max. :52.500 Max. :175.7
## GS GS/G
## Min. :-3.50 Min. :-0.5900
## 1st Qu.: 3.50 1st Qu.: 0.1400
## Median :17.20 Median : 0.3000
## Mean :22.69 Mean : 0.3372
## 3rd Qu.:37.45 3rd Qu.: 0.5100
## Max. :99.20 Max. : 1.2600
cor(NHL$Salary, select_if(NHL, is.numeric))
## Salary Ht Wt DftYr DftRd Ovrl GP
## [1,] 1 0.0725865 0.158679 -0.454342 -0.2368023 -0.2539748 0.469868
## G A A1 A2 PTS PM E+/-
## [1,] 0.5826013 0.6609185 0.6366981 0.6143923 0.6698338 0.1734101 0.2815903
## PIM Shifts TOI TOIX TOI/GP...29 TOI/GP...30 TOI%
## [1,] 0.2606414 0.5712678 0.605303 0.6053201 0.6007812 0.6010984 0.5654077
## IPP% SH% SV% PDO F/60 A/60 Pct%
## [1,] 0.1797133 0.2823685 -0.04531451 0.1820004 0.4131516 -0.01150073 0.2954794
## Diff Diff/60 iCF...41 iCF...42 iFF iSF...44 iSF...45
## [1,] 0.4161073 0.2907968 0.6492011 0.6489927 0.6490971 0.6496799 0.6497235
## iSF...46 ixG iSCF iRB iRS iDS sDist...52
## [1,] 0.6497467 0.5771281 0.4953506 0.4619221 0.5037382 0.5207104 0.02717304
## sDist...53 Pass iHF...55 iHF...56 iHA iHDf iMiss
## [1,] -0.002805594 0.5879846 0.215743 0.2158166 0.3649198 -0.05564978 0.6184659
## iGVA...60 iTKA...61 iBLK...62 iGVA...63 iTKA...64 iBLK...65 BLK%
## [1,] 0.5519523 0.4613922 0.3291048 0.5530128 0.4628361 0.330085 -0.03684297
## iFOW...67 iFOL...68 iFOW...69 iFOL...70 FO% %FOT dzFOW
## [1,] 0.3069584 0.278771 0.3068316 0.2788238 0.0925531 0.06229918 0.2533886
## dzFOL nzFOW nzFOL ozFOW ozFOL FOW.Up FOL.Up
## [1,] 0.2298358 0.2955186 0.2589247 0.3505631 0.3275519 0.2989825 0.268225
## FOW.Down FOL.Down FOW.Close FOL.Close OTG 1G GWG
## [1,] 0.3009973 0.2689279 0.3108253 0.2823277 0.3186809 0.5163133 0.5564102
## ENG PSG PSA G.Bkhd G.Dflct G.Slap G.Snap
## [1,] 0.4295636 0.05974358 0.150269 0.2353363 0.2895829 0.4289538 0.4338371
## G.Tip G.Wrap G.Wrst CBar Post Over Wide
## [1,] 0.3332158 0.1728281 0.5313882 0.2086992 0.4465628 0.4784401 0.6148983
## S.Bkhd S.Dflct S.Slap S.Snap S.Tip S.Wrap S.Wrst
## [1,] 0.4234477 0.3474582 0.4240401 0.4872142 0.4196645 0.2069183 0.5948321
## iPenT iPenD iPENT iPEND iPenDf NPD Min
## [1,] 0.359327 0.3668512 0.3749997 0.3621991 -0.04169453 0.1010064 0.4224469
## Maj Match Misc Game CF CA
## [1,] -0.02850292 -0.03829049 0.07485138 -0.03437022 0.6609512 0.5622878
## FF FA SF SA xGF xGA SCF
## [1,] 0.6592779 0.5639558 0.6650839 0.5695632 0.6771599 0.5588539 0.67518
## SCA GF GA RBF RBA RSF RSA
## [1,] 0.5530132 0.6820274 0.5710731 0.6170984 0.5018589 0.556302 0.5723369
## DSF DSA FOW FOL HF HA GVA
## [1,] 0.6013619 0.5624003 0.6501889 0.6299849 0.4140283 0.5161623 0.5881052
## TKA PENT PEND OPS DPS PS OTOI
## [1,] 0.5600872 0.5277816 0.5901456 0.6333474 0.428782 0.6601165 0.4367475
## Grit DAP Pace GS GS/G
## [1,] 0.3176354 -0.02697638 0.2915016 0.6737828 0.6078714
NHL <- dummy_cols(NHL, select_columns = "Position", remove_first_dummy = TRUE)
model <- lm(Salary ~ GP + GS + PM + PIM + Wt + iHDf + nzFOL + nzFOW + Position_CD + Position_CLW + Position_CRW + Position_CLWRW + Position_D + Position_LW + Position_LWRW + Position_RW, data = NHL)
model
##
## Call:
## lm(formula = Salary ~ GP + GS + PM + PIM + Wt + iHDf + nzFOL +
## nzFOW + Position_CD + Position_CLW + Position_CRW + Position_CLWRW +
## Position_D + Position_LW + Position_LWRW + Position_RW, data = NHL)
##
## Coefficients:
## (Intercept) GP GS PM PIM
## -3450060.1 -6654.8 85395.8 -14366.6 565.3
## Wt iHDf nzFOL nzFOW Position_CD
## 21695.1 2689.0 -16200.9 15434.3 428130.0
## Position_CLW Position_CRW Position_CLWRW Position_D Position_LW
## -540997.2 51321.3 -401640.5 174818.3 -125761.3
## Position_LWRW Position_RW
## 25434.0 -422465.0
standard_error <- sqrt(deviance(model)/df.residual(model))
standard_error
## [1] 1741595
2*standard_error
## [1] 3483190
plot(fitted(model),resid(model))
abline(h=2*standard_error, col = "blue")
abline(h=-2*standard_error, col = "blue")
abline(h=3*standard_error, col = "red")
abline(h=-3*standard_error, col = "red")
res_pot_outliers <- NHL %>% filter(2*standard_error <= abs(resid(model)) & abs(resid(model)) < 3*standard_error)
print(res_pot_outliers)
## # A tibble: 13 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 832500 95-04-… Lond… ON CAN CAN 72 223 2013 1 9 L
## 2 9000000 87-10-… Madi… WI USA USA 72 202 2006 1 5 R
## 3 925000 97-07-… Gros… MI USA USA 74 218 2015 1 8 L
## 4 925000 93-04-… Pemb… FL USA USA 71 180 2012 3 78 L
## 5 7500000 85-04-… Edmo… AB CAN CAN 75 219 2003 1 9 L
## 6 6000000 83-03-… Kitc… ON CAN CAN 72 202 2002 8 241 R
## 7 9000000 85-01-… Madi… WI USA USA 74 206 2003 1 7 L
## 8 925000 93-05-… St. … AB CAN CAN 78 226 2012 3 86 R
## 9 925000 97-12-… Scot… AZ USA USA 74 202 2016 1 6 L
## 10 9000000 84-07-… Minn… MN USA USA 71 196 2003 1 17 L
## 11 832500 95-03-… Ste-… QC CAN CAN 71 188 2013 1 3 L
## 12 8000000 84-06-… Bram… ON CAN CAN 76 212 2002 1 1 L
## 13 8000000 88-04-… St. … MN USA USA 72 218 2006 1 7 R
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, iCF...42 <dbl>,
## # iFF <dbl>, iSF...44 <dbl>, iSF...45 <dbl>, iSF...46 <dbl>, ixG <dbl>, …
res_outliers <- NHL %>% filter(abs(resid(model)) >= 3*standard_error)
print(res_pot_outliers)
## # A tibble: 13 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 832500 95-04-… Lond… ON CAN CAN 72 223 2013 1 9 L
## 2 9000000 87-10-… Madi… WI USA USA 72 202 2006 1 5 R
## 3 925000 97-07-… Gros… MI USA USA 74 218 2015 1 8 L
## 4 925000 93-04-… Pemb… FL USA USA 71 180 2012 3 78 L
## 5 7500000 85-04-… Edmo… AB CAN CAN 75 219 2003 1 9 L
## 6 6000000 83-03-… Kitc… ON CAN CAN 72 202 2002 8 241 R
## 7 9000000 85-01-… Madi… WI USA USA 74 206 2003 1 7 L
## 8 925000 93-05-… St. … AB CAN CAN 78 226 2012 3 86 R
## 9 925000 97-12-… Scot… AZ USA USA 74 202 2016 1 6 L
## 10 9000000 84-07-… Minn… MN USA USA 71 196 2003 1 17 L
## 11 832500 95-03-… Ste-… QC CAN CAN 71 188 2013 1 3 L
## 12 8000000 84-06-… Bram… ON CAN CAN 76 212 2002 1 1 L
## 13 8000000 88-04-… St. … MN USA USA 72 218 2006 1 7 R
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, iCF...42 <dbl>,
## # iFF <dbl>, iSF...44 <dbl>, iSF...45 <dbl>, iSF...46 <dbl>, ixG <dbl>, …
h <- 2*(9+1)/359
h
## [1] 0.05571031
leverage<-hatvalues(model)
sort(round(leverage,4))
## 264 253 216 183 268 247 198 270 214 204 260
## 0.0104 0.0108 0.0119 0.0124 0.0124 0.0126 0.0128 0.0128 0.0129 0.0130 0.0130
## 208 243 180 207 226 194 154 178 196 175 173
## 0.0134 0.0134 0.0138 0.0139 0.0139 0.0140 0.0146 0.0146 0.0146 0.0148 0.0150
## 235 217 236 223 211 252 213 245 256 227 174
## 0.0155 0.0156 0.0158 0.0159 0.0160 0.0160 0.0162 0.0163 0.0164 0.0165 0.0166
## 149 234 239 261 150 262 182 225 195 164 201
## 0.0167 0.0169 0.0169 0.0169 0.0172 0.0177 0.0178 0.0179 0.0181 0.0182 0.0182
## 251 159 176 185 189 165 255 147 169 257 265
## 0.0182 0.0184 0.0184 0.0184 0.0184 0.0189 0.0191 0.0195 0.0195 0.0195 0.0195
## 179 258 155 238 263 172 190 168 209 241 203
## 0.0197 0.0197 0.0200 0.0201 0.0201 0.0203 0.0203 0.0207 0.0212 0.0212 0.0217
## 22 191 222 145 250 160 249 161 272 199 206
## 0.0219 0.0219 0.0220 0.0225 0.0225 0.0230 0.0231 0.0232 0.0235 0.0237 0.0239
## 240 187 156 181 97 58 224 68 202 248 86
## 0.0239 0.0241 0.0245 0.0250 0.0253 0.0257 0.0257 0.0261 0.0261 0.0261 0.0262
## 95 146 212 51 242 266 40 71 89 85 158
## 0.0262 0.0264 0.0264 0.0265 0.0266 0.0267 0.0272 0.0273 0.0273 0.0276 0.0282
## 171 218 200 186 197 210 215 229 21 8 46
## 0.0282 0.0284 0.0285 0.0287 0.0287 0.0290 0.0293 0.0296 0.0302 0.0303 0.0303
## 93 151 184 188 5 53 205 101 237 335 15
## 0.0304 0.0304 0.0304 0.0305 0.0307 0.0308 0.0309 0.0311 0.0311 0.0314 0.0316
## 35 157 244 72 353 49 273 81 167 64 267
## 0.0316 0.0317 0.0318 0.0319 0.0319 0.0320 0.0323 0.0324 0.0324 0.0325 0.0325
## 27 65 7 347 269 221 231 1 74 153 37
## 0.0326 0.0326 0.0327 0.0327 0.0328 0.0331 0.0331 0.0333 0.0333 0.0334 0.0336
## 79 32 84 232 30 342 29 328 26 11 333
## 0.0337 0.0338 0.0338 0.0339 0.0343 0.0344 0.0345 0.0346 0.0347 0.0350 0.0351
## 336 39 177 31 18 45 80 43 102 228 50
## 0.0351 0.0352 0.0352 0.0355 0.0357 0.0358 0.0359 0.0362 0.0364 0.0364 0.0366
## 166 352 340 348 17 230 162 329 2 338 358
## 0.0367 0.0367 0.0368 0.0369 0.0371 0.0372 0.0373 0.0373 0.0375 0.0379 0.0385
## 259 14 285 331 280 220 56 345 325 301 62
## 0.0386 0.0389 0.0392 0.0393 0.0394 0.0395 0.0397 0.0399 0.0400 0.0401 0.0403
## 330 296 289 152 20 54 99 82 276 246 290
## 0.0403 0.0406 0.0410 0.0411 0.0413 0.0414 0.0415 0.0416 0.0416 0.0420 0.0420
## 332 343 9 274 281 300 295 287 298 28 359
## 0.0420 0.0420 0.0421 0.0422 0.0422 0.0422 0.0424 0.0425 0.0428 0.0430 0.0432
## 351 148 163 271 12 91 19 76 44 354 279
## 0.0433 0.0435 0.0438 0.0438 0.0440 0.0440 0.0442 0.0442 0.0444 0.0447 0.0449
## 67 63 254 334 283 13 60 288 48 87 94
## 0.0450 0.0451 0.0453 0.0458 0.0459 0.0460 0.0462 0.0465 0.0466 0.0469 0.0469
## 193 341 119 278 38 123 69 337 16 78 138
## 0.0469 0.0469 0.0472 0.0473 0.0476 0.0479 0.0482 0.0488 0.0489 0.0491 0.0492
## 299 303 92 233 96 293 327 66 36 88 170
## 0.0492 0.0492 0.0501 0.0505 0.0508 0.0511 0.0514 0.0515 0.0516 0.0518 0.0519
## 355 356 134 297 320 133 142 33 127 292 304
## 0.0519 0.0521 0.0526 0.0534 0.0537 0.0538 0.0540 0.0541 0.0542 0.0549 0.0553
## 275 319 55 100 144 77 312 129 126 357 291
## 0.0555 0.0557 0.0562 0.0564 0.0567 0.0568 0.0568 0.0569 0.0570 0.0570 0.0575
## 316 309 350 310 4 75 143 314 90 61 346
## 0.0578 0.0582 0.0587 0.0589 0.0591 0.0592 0.0592 0.0597 0.0604 0.0606 0.0606
## 141 192 344 118 120 313 42 305 139 323 3
## 0.0610 0.0612 0.0612 0.0623 0.0624 0.0624 0.0626 0.0632 0.0635 0.0650 0.0652
## 122 308 121 282 318 349 339 6 135 73 306
## 0.0660 0.0662 0.0663 0.0666 0.0670 0.0683 0.0684 0.0689 0.0689 0.0691 0.0695
## 284 108 131 47 116 302 112 109 307 70 114
## 0.0696 0.0704 0.0706 0.0714 0.0721 0.0726 0.0734 0.0749 0.0751 0.0752 0.0754
## 124 113 110 294 130 117 115 104 140 107 23
## 0.0755 0.0760 0.0768 0.0778 0.0784 0.0807 0.0812 0.0823 0.0824 0.0825 0.0842
## 311 103 106 324 326 57 317 111 277 321 136
## 0.0850 0.0858 0.0869 0.0876 0.0887 0.0893 0.0900 0.0901 0.0903 0.0908 0.0925
## 286 128 137 315 34 105 83 24 98 132 219
## 0.0942 0.0967 0.0983 0.0983 0.1017 0.1063 0.1095 0.1146 0.1162 0.1172 0.1187
## 322 59 10 25 125 41 52
## 0.1214 0.1269 0.1400 0.1402 0.1716 0.2605 1.0000
leverage_outliers <- NHL %>% filter(leverage > h)
leverage_outliers
## # A tibble: 93 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 1000000 88-03… Bran… MB CAN CAN 72 200 2006 3 66 R
## 2 925000 96-06… Holl… ON CAN CAN 73 186 2014 1 4 L
## 3 6000000 90-09… Miss… ON CAN CAN 73 211 2009 1 1 L
## 4 10900000 87-08… Cole… NS CAN CAN 71 200 2005 1 1 L
## 5 2075000 91-12… St. … ON CAN CAN 75 226 2010 1 21 L
## 6 7000000 85-12… Queb… QC CAN USA 72 202 2005 2 44 L
## 7 5000000 93-03… Kitc… ON CAN CAN 75 207 2011 1 7 R
## 8 925000 96-10… Nort… MA USA USA 74 196 2015 1 2 R
## 9 8750000 85-07… Anci… QC CAN CAN 73 195 2003 2 45 R
## 10 1100000 92-11… Otta… ON CAN CAN 70 180 2011 4 96 R
## # ℹ 83 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
t <- qt(df = 359 - 9 - 2, 0.95)
t
## [1] 1.649244
jackknife <- rstudent(model)
sort(round(jackknife, 4))
## 188 277 36 273 291 193 96 282 153 166
## -2.7595 -2.4562 -2.4408 -2.2173 -2.2088 -2.1708 -1.9759 -1.9366 -1.9287 -1.9143
## 261 254 34 212 136 98 205 167 12 141
## -1.8080 -1.7771 -1.7678 -1.6064 -1.5266 -1.5190 -1.5067 -1.4453 -1.4067 -1.3954
## 5 343 230 317 312 354 42 13 118 105
## -1.3940 -1.3583 -1.3459 -1.3329 -1.3056 -1.2991 -1.2601 -1.1910 -1.1874 -1.1834
## 342 255 178 323 355 245 64 198 172 151
## -1.1744 -1.1718 -1.1154 -1.1069 -1.0964 -1.0758 -1.0393 -1.0280 -1.0189 -1.0047
## 232 256 79 226 51 72 154 242 162 260
## -0.9999 -0.9868 -0.9501 -0.9431 -0.9362 -0.9360 -0.9097 -0.9091 -0.8968 -0.8818
## 112 77 335 53 258 339 220 270 359 249
## -0.8782 -0.8517 -0.8314 -0.8281 -0.8168 -0.8144 -0.7986 -0.7920 -0.7732 -0.7604
## 303 210 310 69 351 73 108 117 80 211
## -0.7588 -0.7496 -0.7340 -0.7237 -0.7224 -0.6988 -0.6988 -0.6632 -0.6555 -0.6541
## 327 131 290 221 43 170 294 197 239 213
## -0.6499 -0.6430 -0.6351 -0.6099 -0.5881 -0.5845 -0.5837 -0.5802 -0.5751 -0.5716
## 164 223 4 299 194 233 301 302 219 275
## -0.5605 -0.5576 -0.5544 -0.5441 -0.5436 -0.5346 -0.5330 -0.5326 -0.5091 -0.5029
## 243 329 143 322 2 321 60 41 130 122
## -0.5012 -0.5009 -0.4901 -0.4901 -0.4882 -0.4845 -0.4816 -0.4813 -0.4660 -0.4656
## 196 92 346 135 307 3 169 168 150 344
## -0.4520 -0.4507 -0.4463 -0.4455 -0.4445 -0.4405 -0.4271 -0.4160 -0.4124 -0.4075
## 216 280 19 201 247 349 90 33 326 179
## -0.3994 -0.3915 -0.3872 -0.3869 -0.3839 -0.3787 -0.3696 -0.3688 -0.3587 -0.3579
## 126 234 28 206 353 123 330 110 189 251
## -0.3549 -0.3483 -0.3474 -0.3393 -0.3380 -0.3368 -0.3353 -0.3317 -0.3316 -0.3134
## 38 314 127 182 207 276 158 87 121 285
## -0.3082 -0.2995 -0.2911 -0.2826 -0.2714 -0.2714 -0.2693 -0.2653 -0.2617 -0.2593
## 6 278 106 227 68 246 257 16 304 236
## -0.2515 -0.2472 -0.2412 -0.2381 -0.2361 -0.2342 -0.2320 -0.2284 -0.2268 -0.2246
## 316 308 133 333 175 263 50 81 37 8
## -0.2058 -0.1985 -0.1949 -0.1927 -0.1909 -0.1878 -0.1825 -0.1782 -0.1759 -0.1723
## 250 298 324 46 149 292 142 202 17 58
## -0.1681 -0.1670 -0.1655 -0.1610 -0.1534 -0.1415 -0.1392 -0.1388 -0.1384 -0.1380
## 29 195 18 94 305 337 295 289 208 148
## -0.1365 -0.1359 -0.1334 -0.1221 -0.1217 -0.1203 -0.1188 -0.1095 -0.1076 -0.0989
## 159 183 23 7 225 132 311 191 27 274
## -0.0958 -0.0894 -0.0818 -0.0786 -0.0746 -0.0727 -0.0707 -0.0698 -0.0655 -0.0649
## 181 296 49 199 352 173 57 124 334 62
## -0.0531 -0.0514 -0.0511 -0.0486 -0.0483 -0.0429 -0.0399 -0.0389 -0.0382 -0.0381
## 174 75 345 32 144 95 119 128 265 85
## -0.0348 -0.0347 -0.0310 -0.0279 -0.0267 -0.0258 -0.0186 0.0021 0.0043 0.0058
## 155 111 177 40 134 287 63 21 336 76
## 0.0059 0.0066 0.0099 0.0118 0.0120 0.0126 0.0145 0.0219 0.0230 0.0461
## 138 145 15 113 340 25 203 30 129 11
## 0.0493 0.0508 0.0586 0.0597 0.0793 0.0828 0.0862 0.0881 0.0916 0.0933
## 348 267 338 328 88 26 152 204 83 146
## 0.1015 0.1057 0.1095 0.1161 0.1242 0.1246 0.1334 0.1435 0.1569 0.1757
## 103 39 67 224 35 306 116 61 93 288
## 0.1837 0.1881 0.1904 0.2139 0.2160 0.2173 0.2195 0.2264 0.2268 0.2270
## 209 115 120 313 347 331 222 45 86 1
## 0.2286 0.2302 0.2413 0.2422 0.2423 0.2428 0.2483 0.2581 0.2600 0.2624
## 56 184 114 78 252 101 71 91 156 82
## 0.2624 0.2696 0.2745 0.2751 0.2836 0.2842 0.2848 0.2907 0.3093 0.3114
## 235 104 84 54 48 74 89 70 125 20
## 0.3400 0.3450 0.3483 0.3705 0.3728 0.3849 0.3926 0.4159 0.4394 0.4742
## 214 192 253 100 65 248 357 97 262 272
## 0.4930 0.5238 0.5304 0.5449 0.5453 0.5574 0.5752 0.5806 0.5840 0.6198
## 66 190 318 283 160 297 268 217 44 341
## 0.6296 0.6354 0.6518 0.6768 0.6788 0.6827 0.7645 0.7841 0.7873 0.8113
## 147 200 165 171 315 269 107 356 286 31
## 0.8619 0.8683 0.8838 0.9318 0.9757 0.9800 0.9969 0.9988 1.0022 1.0086
## 332 320 241 24 157 266 59 244 293 102
## 1.0093 1.0419 1.0541 1.0716 1.0723 1.1043 1.1180 1.1195 1.1297 1.1556
## 185 161 9 55 284 180 14 163 237 350
## 1.1887 1.1973 1.2574 1.2753 1.3140 1.3252 1.3668 1.3811 1.4183 1.4357
## 187 279 140 238 240 215 309 109 22 231
## 1.4382 1.4418 1.4483 1.5301 1.5704 1.5794 1.6624 1.6697 1.7553 1.7764
## 218 99 176 229 264 139 10 319 228 325
## 1.7924 1.8187 1.9310 1.9710 2.0678 2.0937 2.1481 2.3761 2.4982 2.5899
## 281 271 300 186 358 259 137 47
## 2.8527 2.9579 3.1425 3.2433 3.6479 3.7598 4.1786 4.8029
jackknife_outliers <- NHL %>% filter(jackknife > t | jackknife < -t)
jackknife_outliers
## # A tibble: 35 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 10900000 87-08… Cole… NS CAN CAN 71 200 2005 1 1 L
## 2 5000000 87-01… St. … MB CAN CAN 72 196 2005 5 132 L
## 3 925000 96-10… Nort… MA USA USA 74 196 2015 1 2 R
## 4 832500 95-04… Lond… ON CAN CAN 72 223 2013 1 9 L
## 5 13800000 88-04… Winn… MB CAN CAN 74 201 2006 1 3 L
## 6 875000 93-02… Vict… QC CAN CAN 73 193 2011 1 26 L
## 7 6500000 84-03… Winn… MB CAN SWE 72 211 2002 1 24 L
## 8 3650000 89-10… Edmo… AB CAN CAN 69 175 2008 1 26 L
## 9 13800000 88-11… Buff… NY USA USA 71 177 2007 1 1 L
## 10 9000000 87-10… Madi… WI USA USA 72 202 2006 1 5 R
## # ℹ 25 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
cookCV <- 4/359
cookCV
## [1] 0.01114206
cook <- cooks.distance(model)
sort(round(cook, 4))
## 7 11 15 17 18 21 23 26 27 29 30
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 32 40 46 49 57 58 62 63 75 76 85
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 88 94 95 111 113 119 124 128 129 132 134
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 138 144 145 146 148 149 152 155 159 173 174
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 175 177 181 183 191 195 199 202 203 204 208
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 225 236 250 263 265 267 274 287 289 295 296
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 311 328 334 336 337 338 340 345 348 352 1
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001
## 8 25 35 37 39 45 50 67 68 71 81
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 86 93 133 142 156 158 182 184 189 207 209
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 216 222 224 227 234 235 246 247 251 252 257
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 288 292 298 305 331 333 347 16 56 61 78
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 0.0002 0.0002
## 82 83 87 91 101 103 116 120 150 168 169
## 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
## 179 194 196 201 206 214 243 253 276 278 285
## 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
## 304 306 308 313 316 324 353 6 28 38 54
## 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0003 0.0003 0.0003 0.0003
## 74 84 89 106 115 121 123 127 164 213 223
## 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
## 239 314 330 19 48 114 126 211 262 268 280
## 0.0003 0.0003 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004
## 2 33 90 97 110 190 248 270 272 20 65
## 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0006 0.0006
## 92 104 160 197 217 260 329 344 349 60 154
## 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007 0.0007
## 226 301 326 3 43 70 198 221 249 258 346
## 0.0007 0.0007 0.0007 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008
## 80 122 135 143 147 165 233 275 299 307 100
## 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0010
## 210 256 290 4 130 170 178 192 245 357 53
## 0.0010 0.0010 0.0010 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0012 0.0013
## 66 172 200 242 283 302 327 335 51 180 241
## 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 0.0014 0.0014 0.0014
## 321 351 171 220 297 69 185 255 359 44 72
## 0.0014 0.0014 0.0015 0.0015 0.0015 0.0016 0.0016 0.0016 0.0016 0.0017 0.0017
## 294 79 162 303 318 131 151 269 341 161 266
## 0.0017 0.0018 0.0018 0.0018 0.0018 0.0019 0.0019 0.0019 0.0019 0.0020 0.0020
## 310 322 64 73 219 232 31 108 157 117 125
## 0.0020 0.0020 0.0021 0.0021 0.0021 0.0021 0.0022 0.0022 0.0022 0.0023 0.0024
## 244 77 264 332 238 339 342 102 187 356 261
## 0.0024 0.0026 0.0026 0.0026 0.0028 0.0029 0.0029 0.0030 0.0030 0.0032 0.0033
## 240 5 112 320 237 355 13 22 293 9 167
## 0.0035 0.0036 0.0036 0.0036 0.0038 0.0039 0.0040 0.0040 0.0040 0.0041 0.0041
## 176 212 230 205 14 215 354 343 41 323 163
## 0.0041 0.0041 0.0041 0.0042 0.0044 0.0044 0.0046 0.0047 0.0048 0.0050 0.0051
## 12 107 118 218 55 279 312 286 315 42 231
## 0.0053 0.0053 0.0055 0.0055 0.0057 0.0057 0.0060 0.0061 0.0061 0.0062 0.0063
## 229 141 153 350 284 166 99 24 254 273 105
## 0.0069 0.0074 0.0075 0.0075 0.0076 0.0082 0.0084 0.0087 0.0088 0.0095 0.0098
## 309 317 59 140 96 109 193 228 188 136 282
## 0.0100 0.0103 0.0107 0.0110 0.0122 0.0132 0.0135 0.0137 0.0138 0.0139 0.0156
## 325 139 291 98 186 36 319 34 281 271 300
## 0.0162 0.0173 0.0173 0.0178 0.0178 0.0188 0.0193 0.0207 0.0207 0.0231 0.0249
## 358 259 277 10 47 137
## 0.0303 0.0322 0.0347 0.0437 0.0980 0.1068
cook_outliers <- NHL %>% filter(cook > cookCV)
cook_outliers
## # A tibble: 24 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 10900000 87-08… Cole… NS CAN CAN 71 200 2005 1 1 L
## 2 925000 96-10… Nort… MA USA USA 74 196 2015 1 2 R
## 3 832500 95-04… Lond… ON CAN CAN 72 223 2013 1 9 L
## 4 13800000 88-04… Winn… MB CAN CAN 74 201 2006 1 3 L
## 5 875000 93-02… Vict… QC CAN CAN 73 193 2011 1 26 L
## 6 5000000 88-05… Hali… NS CAN CAN 69 181 2006 3 71 L
## 7 3650000 89-10… Edmo… AB CAN CAN 69 175 2008 1 26 L
## 8 3750000 93-07… Pitt… PA USA USA 70 182 2011 3 64 R
## 9 13800000 88-11… Buff… NY USA USA 71 177 2007 1 1 L
## 10 9000000 87-10… Madi… WI USA USA 72 202 2006 1 5 R
## # ℹ 14 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
ggplot(NHL, aes(x = fitted(model), y = jackknife)) + geom_point()+ geom_hline(yintercept = t, col = "purple") + geom_hline(yintercept = -t, col = "purple")
## Warning: Removed 1 rows containing missing values (`geom_point()`).
qqnorm(resid(model))
qqline(resid(model), col = "red", lwd = 2)
qqPlot(resid(model))
## [1] 47 137
skewness(jackknife)
## [1] NaN
kurtosis(jackknife)
## [1] NaN
ols_vif_tol(model)
## Variables Tolerance VIF
## 1 GP 0.32530307 3.074056
## 2 GS 0.33739699 2.963868
## 3 PM 0.83670390 1.195166
## 4 PIM 0.44604534 2.241925
## 5 Wt 0.78070556 1.280893
## 6 iHDf 0.56448288 1.771533
## 7 nzFOL 0.05681488 17.601023
## 8 nzFOW 0.05846768 17.103466
## 9 Position_CD 0.96845535 1.032572
## 10 Position_CLW 0.51962206 1.924476
## 11 Position_CRW 0.67122489 1.489814
## 12 Position_CLWRW 0.66995728 1.492632
## 13 Position_D 0.27757891 3.602579
## 14 Position_LW 0.52569223 1.902254
## 15 Position_LWRW 0.58763057 1.701749
## 16 Position_RW 0.49775543 2.009019
eigprop(model)
##
## Call:
## eigprop(mod = model)
##
## Eigenvalues CI (Intercept) GP GS PM PIM Wt iHDf
## 1 5.6564 1.0000 0.0001 0.0021 0.0038 0.0000 0.0044 0.0001 0.0005
## 2 1.8655 1.7413 0.0001 0.0002 0.0008 0.0016 0.0034 0.0001 0.0194
## 3 1.3501 2.0469 0.0000 0.0002 0.0041 0.1826 0.0020 0.0000 0.1299
## 4 1.0542 2.3164 0.0000 0.0000 0.0003 0.1263 0.0007 0.0000 0.0348
## 5 1.0108 2.3656 0.0000 0.0002 0.0010 0.0003 0.0001 0.0000 0.0000
## 6 1.0089 2.3679 0.0000 0.0000 0.0003 0.0010 0.0015 0.0000 0.0000
## 7 1.0004 2.3779 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 8 1.0000 2.3783 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 9 0.9023 2.5037 0.0000 0.0001 0.0053 0.2810 0.0008 0.0000 0.0006
## 10 0.8038 2.6527 0.0001 0.0000 0.0011 0.1153 0.0141 0.0001 0.2767
## 11 0.7166 2.8096 0.0000 0.0000 0.0001 0.0672 0.0000 0.0000 0.0061
## 12 0.3286 4.1491 0.0016 0.0155 0.1306 0.1517 0.1234 0.0015 0.0238
## 13 0.1560 6.0224 0.0000 0.0024 0.3644 0.0315 0.6183 0.0000 0.4358
## 14 0.0655 9.2896 0.0069 0.1762 0.0204 0.0044 0.0529 0.0060 0.0069
## 15 0.0542 10.2133 0.0055 0.7821 0.4601 0.0295 0.1649 0.0054 0.0000
## 16 0.0245 15.1952 0.0001 0.0202 0.0075 0.0052 0.0065 0.0001 0.0025
## 17 0.0022 50.8512 0.9854 0.0006 0.0002 0.0023 0.0069 0.9866 0.0629
## nzFOL nzFOW Position_CD Position_CLW Position_CRW Position_CLWRW
## 1 0.0006 0.0006 0.0000 0.0023 0.0021 0.0007
## 2 0.0067 0.0072 0.0001 0.0047 0.0233 0.0017
## 3 0.0005 0.0006 0.0001 0.0002 0.0062 0.0029
## 4 0.0000 0.0001 0.0088 0.0813 0.0593 0.0472
## 5 0.0000 0.0000 0.2844 0.0020 0.0139 0.1924
## 6 0.0000 0.0000 0.0677 0.0782 0.0570 0.3250
## 7 0.0000 0.0000 0.1047 0.0807 0.0865 0.0110
## 8 0.0000 0.0000 0.4803 0.0012 0.0009 0.0009
## 9 0.0000 0.0001 0.0083 0.0002 0.0473 0.0000
## 10 0.0004 0.0007 0.0039 0.0034 0.0308 0.0168
## 11 0.0057 0.0061 0.0002 0.1872 0.3437 0.0007
## 12 0.0045 0.0044 0.0081 0.0115 0.0035 0.0238
## 13 0.0006 0.0006 0.0001 0.0108 0.0112 0.0110
## 14 0.0013 0.0249 0.0168 0.4729 0.2258 0.3302
## 15 0.0059 0.0000 0.0123 0.0548 0.0719 0.0260
## 16 0.9732 0.9547 0.0001 0.0001 0.0130 0.0032
## 17 0.0005 0.0001 0.0040 0.0085 0.0034 0.0065
## Position_D Position_LW Position_LWRW Position_RW
## 1 0.0014 0.0010 0.0010 0.0010
## 2 0.0092 0.0101 0.0093 0.0078
## 3 0.0184 0.0335 0.0186 0.0004
## 4 0.0033 0.0076 0.0035 0.1435
## 5 0.0105 0.0551 0.0945 0.0030
## 6 0.0013 0.0214 0.0466 0.0000
## 7 0.0217 0.0001 0.0430 0.1590
## 8 0.0002 0.0820 0.1745 0.0046
## 9 0.0182 0.1826 0.0466 0.0285
## 10 0.0079 0.0520 0.0702 0.0473
## 11 0.0097 0.0001 0.0004 0.0097
## 12 0.0112 0.0128 0.0420 0.0066
## 13 0.0142 0.0003 0.0019 0.0001
## 14 0.7556 0.4274 0.3926 0.4961
## 15 0.0916 0.1056 0.0496 0.0861
## 16 0.0157 0.0053 0.0051 0.0055
## 17 0.0098 0.0031 0.0005 0.0006
##
## ===============================
## Row 15==> GP, proportion 0.782132 >= 0.50
## Row 13==> PIM, proportion 0.618316 >= 0.50
## Row 17==> Wt, proportion 0.986597 >= 0.50
## Row 16==> nzFOL, proportion 0.973174 >= 0.50
## Row 16==> nzFOW, proportion 0.954652 >= 0.50
## Row 14==> Position_D, proportion 0.755555 >= 0.50
ols_step_forward_p(model)
##
## Selection Summary
## -------------------------------------------------------------------------------------
## Variable Adj.
## Step Entered R-Square R-Square C(p) AIC RMSE
## -------------------------------------------------------------------------------------
## 1 GS 0.4540 0.4525 27.1705 11365.1352 1801945.3109
## 2 Wt 0.4811 0.4781 10.2252 11348.8823 1759179.4048
## 3 Position_CLW 0.4889 0.4846 6.7203 11345.3998 1748254.9274
## 4 Position_RW 0.4922 0.4865 6.4045 11345.0682 1745046.4442
## 5 iHDf 0.4941 0.4870 7.0724 11345.7201 1744238.3455
## 6 GP 0.4965 0.4879 7.4011 11346.0214 1742586.7942
## 7 PM 0.4983 0.4883 8.1385 11346.7329 1741938.5202
## 8 Position_D 0.5002 0.4888 8.8278 11347.3904 1741166.5170
## -------------------------------------------------------------------------------------
ols_step_backward_p(model)
##
##
## Elimination Summary
## ---------------------------------------------------------------------------------------
## Variable Adj.
## Step Removed R-Square R-Square C(p) AIC RMSE
## ---------------------------------------------------------------------------------------
## 1 Position_LWRW 0.5114 0.490 15.0025 11353.2687 1739060.5871
## 2 PIM 0.5114 0.4915 13.0139 11351.2807 1736560.1588
## 3 Position_CRW 0.5113 0.4929 11.0241 11349.2914 1734067.2801
## 4 Position_CD 0.5113 0.4943 9.0780 11347.3480 1731696.0967
## 5 Position_LW 0.511 0.4955 7.2296 11345.5070 1729582.0861
## 6 Position_CLWRW 0.5102 0.4961 5.8561 11344.1636 1728675.4796
## 7 Position_RW 0.5087 0.496 4.9078 11343.2632 1728842.6744
## ---------------------------------------------------------------------------------------
ols_step_both_p(model)
##
## Stepwise Selection Summary
## -------------------------------------------------------------------------------------------------
## Added/ Adj.
## Step Variable Removed R-Square R-Square C(p) AIC RMSE
## -------------------------------------------------------------------------------------------------
## 1 GS addition 0.454 0.452 27.1700 11365.1352 1801945.3109
## 2 Wt addition 0.481 0.478 10.2250 11348.8823 1759179.4048
## 3 Position_CLW addition 0.489 0.485 6.7200 11345.3998 1748254.9274
## -------------------------------------------------------------------------------------------------
NHL2 <- select(NHL,c(GP,GS, PM, PIM, Wt, iHDf, nzFOL, nzFOW))
NHL2
## # A tibble: 359 × 8
## GP GS PM PIM Wt iHDf nzFOL nzFOW
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 10 2.1 -3 2 178 -7 17 13
## 2 68 5.7 -12 29 204 16 70 86
## 3 65 7.8 -16 84 200 118 7 9
## 4 81 21.6 -16 75 186 61 163 141
## 5 70 29.3 -15 25 196 29 108 105
## 6 77 75.9 4 38 211 -26 237 212
## 7 12 3.3 1 2 195 3 0 0
## 8 9 2.2 0 9 199 1 19 13
## 9 46 21.1 -5 14 179 -5 106 70
## 10 75 94.6 17 24 200 -11 326 293
## # ℹ 349 more rows
pairs.panels(NHL2)
model2 <- lm(Salary ~ GS + Wt + iHDf + GP + PM + Position_CD + Position_CLW + Position_CRW + Position_CLWRW + Position_D + Position_LW + Position_LWRW + Position_RW, data = NHL)
model2
##
## Call:
## lm(formula = Salary ~ GS + Wt + iHDf + GP + PM + Position_CD +
## Position_CLW + Position_CRW + Position_CLWRW + Position_D +
## Position_LW + Position_LWRW + Position_RW, data = NHL)
##
## Coefficients:
## (Intercept) GS Wt iHDf GP
## -3455138 86695 21532 3361 -7212
## PM Position_CD Position_CLW Position_CRW Position_CLWRW
## -12405 445563 -589433 139216 -400945
## Position_D Position_LW Position_LWRW Position_RW
## 231137 -93524 59180 -399269
standard_error2 <- sqrt(deviance(model2)/df.residual(model2))
standard_error2
## [1] 1750959
2*standard_error2
## [1] 3501919
plot(fitted(model2),resid(model2))
abline(h=2*standard_error2, col = "blue")
abline(h=-2*standard_error2, col = "blue")
abline(h=3*standard_error2, col = "red")
abline(h=-3*standard_error2, col = "red")
res_pot_outliers2 <- NHL %>% filter(2*standard_error2 <= abs(resid(model2)) & abs(resid(model2)) < 3*standard_error2)
print(res_pot_outliers2)
## # A tibble: 13 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 925000 96-10-… Nort… MA USA USA 74 196 2015 1 2 R
## 2 832500 95-04-… Lond… ON CAN CAN 72 223 2013 1 9 L
## 3 925000 97-07-… Gros… MI USA USA 74 218 2015 1 8 L
## 4 925000 93-04-… Pemb… FL USA USA 71 180 2012 3 78 L
## 5 7500000 85-04-… Edmo… AB CAN CAN 75 219 2003 1 9 L
## 6 6000000 83-03-… Kitc… ON CAN CAN 72 202 2002 8 241 R
## 7 9000000 85-01-… Madi… WI USA USA 74 206 2003 1 7 L
## 8 925000 93-05-… St. … AB CAN CAN 78 226 2012 3 86 R
## 9 925000 97-12-… Scot… AZ USA USA 74 202 2016 1 6 L
## 10 9000000 84-07-… Minn… MN USA USA 71 196 2003 1 17 L
## 11 832500 95-03-… Ste-… QC CAN CAN 71 188 2013 1 3 L
## 12 8000000 84-06-… Bram… ON CAN CAN 76 212 2002 1 1 L
## 13 8000000 88-04-… St. … MN USA USA 72 218 2006 1 7 R
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, iCF...42 <dbl>,
## # iFF <dbl>, iSF...44 <dbl>, iSF...45 <dbl>, iSF...46 <dbl>, ixG <dbl>, …
res_outliers2 <- NHL %>% filter(abs(resid(model2)) >= 3*standard_error2)
print(res_outliers2)
## # A tibble: 6 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 13800000 88-04-… Winn… MB CAN CAN 74 201 2006 1 3 L
## 2 13800000 88-11-… Buff… NY USA USA 71 177 2007 1 1 L
## 3 11000000 89-05-… Toro… ON CAN CAN 72 210 2007 2 43 R
## 4 12000000 85-08-… Sica… BC CAN CAN 76 232 2003 2 49 R
## 5 8000000 85-12-… Mapl… BC CAN CAN 75 200 2004 1 4 L
## 6 6500000 85-03-… Roch… NY USA USA 70 187 2004 4 127 R
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, iCF...42 <dbl>,
## # iFF <dbl>, iSF...44 <dbl>, iSF...45 <dbl>, iSF...46 <dbl>, ixG <dbl>, …
h2 <- 2*(6+1)/359
h2
## [1] 0.03899721
leverage2 <- hatvalues(model2)
sort(round(leverage2,4))
## 197 243 253 264 216 198 183 214 196 247 174
## 0.0093 0.0093 0.0100 0.0100 0.0106 0.0108 0.0114 0.0116 0.0118 0.0118 0.0119
## 268 204 225 260 270 180 208 154 207 226 175
## 0.0120 0.0122 0.0125 0.0125 0.0125 0.0126 0.0126 0.0128 0.0131 0.0131 0.0133
## 156 194 249 173 252 213 235 178 211 236 223
## 0.0136 0.0137 0.0137 0.0138 0.0139 0.0141 0.0141 0.0142 0.0145 0.0148 0.0151
## 261 217 228 227 149 161 239 150 165 184 245
## 0.0151 0.0153 0.0153 0.0156 0.0157 0.0157 0.0158 0.0159 0.0160 0.0160 0.0160
## 256 176 234 182 195 185 201 251 159 164 172
## 0.0161 0.0162 0.0164 0.0167 0.0168 0.0169 0.0169 0.0169 0.0170 0.0170 0.0172
## 189 262 255 187 203 257 155 241 265 179 263
## 0.0172 0.0173 0.0175 0.0176 0.0182 0.0184 0.0185 0.0185 0.0185 0.0187 0.0187
## 218 238 258 169 147 168 190 191 209 22 145
## 0.0188 0.0188 0.0188 0.0190 0.0194 0.0196 0.0196 0.0201 0.0206 0.0207 0.0209
## 250 231 206 222 272 160 199 58 151 68 242
## 0.0209 0.0210 0.0212 0.0212 0.0212 0.0219 0.0219 0.0221 0.0222 0.0226 0.0226
## 24 73 181 248 212 240 188 49 51 46 85
## 0.0228 0.0231 0.0232 0.0232 0.0233 0.0233 0.0236 0.0238 0.0240 0.0242 0.0244
## 14 158 7 266 21 146 224 53 202 97 9
## 0.0245 0.0246 0.0248 0.0248 0.0249 0.0250 0.0250 0.0251 0.0251 0.0252 0.0254
## 8 171 86 95 96 15 186 200 38 71 87
## 0.0255 0.0255 0.0256 0.0256 0.0257 0.0258 0.0258 0.0258 0.0259 0.0260 0.0260
## 89 37 63 29 18 40 50 27 80 43 30
## 0.0260 0.0261 0.0261 0.0264 0.0266 0.0271 0.0271 0.0272 0.0272 0.0273 0.0274
## 35 64 32 45 210 79 26 215 5 230 11
## 0.0276 0.0277 0.0279 0.0281 0.0282 0.0283 0.0284 0.0285 0.0287 0.0288 0.0290
## 72 19 48 229 84 101 102 1 93 78 83
## 0.0290 0.0291 0.0292 0.0292 0.0293 0.0293 0.0293 0.0294 0.0294 0.0297 0.0298
## 167 267 61 205 31 81 273 335 162 244 353
## 0.0300 0.0302 0.0303 0.0304 0.0305 0.0305 0.0306 0.0307 0.0309 0.0309 0.0309
## 166 237 269 75 157 153 342 65 20 347 2
## 0.0310 0.0310 0.0310 0.0313 0.0314 0.0315 0.0318 0.0319 0.0320 0.0320 0.0323
## 62 221 232 74 329 259 177 54 99 17 39
## 0.0324 0.0326 0.0327 0.0329 0.0329 0.0330 0.0332 0.0333 0.0338 0.0340 0.0341
## 328 333 336 152 352 36 28 67 16 47 82
## 0.0341 0.0341 0.0342 0.0344 0.0344 0.0349 0.0350 0.0350 0.0351 0.0352 0.0353
## 91 340 44 220 348 358 332 233 34 12 280
## 0.0353 0.0356 0.0358 0.0358 0.0358 0.0363 0.0364 0.0365 0.0366 0.0367 0.0368
## 338 13 56 301 285 331 343 57 94 345 293
## 0.0368 0.0371 0.0371 0.0374 0.0375 0.0378 0.0378 0.0385 0.0386 0.0388 0.0391
## 325 42 330 354 355 60 296 289 4 276 359
## 0.0391 0.0393 0.0397 0.0398 0.0398 0.0399 0.0401 0.0402 0.0407 0.0407 0.0407
## 92 271 281 287 274 124 295 246 290 300 341
## 0.0409 0.0409 0.0409 0.0409 0.0411 0.0414 0.0414 0.0415 0.0415 0.0417 0.0417
## 254 298 148 299 351 163 66 100 76 139 6
## 0.0418 0.0418 0.0425 0.0427 0.0427 0.0429 0.0432 0.0432 0.0434 0.0434 0.0438
## 69 55 123 283 279 193 288 357 334 3 119
## 0.0441 0.0443 0.0444 0.0444 0.0447 0.0449 0.0449 0.0449 0.0450 0.0451 0.0452
## 286 326 125 133 138 278 90 277 303 327 33
## 0.0452 0.0452 0.0453 0.0458 0.0465 0.0466 0.0470 0.0470 0.0470 0.0470 0.0474
## 350 134 337 127 25 88 297 118 144 346 356
## 0.0474 0.0475 0.0477 0.0481 0.0486 0.0488 0.0489 0.0500 0.0502 0.0505 0.0511
## 130 132 142 170 320 292 77 344 141 41 275
## 0.0514 0.0514 0.0514 0.0517 0.0517 0.0519 0.0520 0.0520 0.0523 0.0526 0.0527
## 291 304 129 319 126 128 312 310 294 143 121
## 0.0529 0.0529 0.0530 0.0530 0.0535 0.0548 0.0548 0.0550 0.0554 0.0555 0.0572
## 316 135 309 314 313 120 284 318 305 192 307
## 0.0574 0.0580 0.0581 0.0581 0.0598 0.0600 0.0600 0.0605 0.0606 0.0611 0.0614
## 323 349 70 282 308 339 122 140 136 131 306
## 0.0615 0.0617 0.0619 0.0620 0.0626 0.0629 0.0636 0.0641 0.0644 0.0669 0.0670
## 324 10 108 302 137 23 116 98 311 114 112
## 0.0676 0.0685 0.0691 0.0699 0.0703 0.0711 0.0715 0.0720 0.0724 0.0726 0.0731
## 113 109 110 107 321 219 117 115 104 106 322
## 0.0739 0.0745 0.0753 0.0759 0.0761 0.0764 0.0769 0.0784 0.0786 0.0804 0.0820
## 103 59 111 315 317 105 52
## 0.0836 0.0839 0.0856 0.0857 0.0883 0.1058 1.0000
leverage_outliers2 <- NHL %>% filter(leverage2 > h2)
leverage_outliers2
## # A tibble: 140 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 1000000 88-03… Bran… MB CAN CAN 72 200 2006 3 66 R
## 2 925000 96-06… Holl… ON CAN CAN 73 186 2014 1 4 L
## 3 6000000 90-09… Miss… ON CAN CAN 73 211 2009 1 1 L
## 4 10900000 87-08… Cole… NS CAN CAN 71 200 2005 1 1 L
## 5 2075000 91-12… St. … ON CAN CAN 75 226 2010 1 21 L
## 6 5000000 93-03… Kitc… ON CAN CAN 75 207 2011 1 7 R
## 7 832500 95-04… St-L… QC CAN CAN 77 235 2013 1 21 L
## 8 8750000 85-07… Anci… QC CAN CAN 73 195 2003 2 45 R
## 9 1100000 92-11… Otta… ON CAN CAN 70 180 2011 4 96 R
## 10 925000 97-01… Bost… MA USA USA 72 183 2015 1 21 R
## # ℹ 130 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
t2 <- qt(df = 359 - 6 - 2, 0.95)
t2
## [1] 1.649206
jackknife2 <- rstudent(model2)
sort(round(jackknife2, 4))
## 188 277 34 36 291 273 193 282 153 166
## -2.7636 -2.3960 -2.3715 -2.3343 -2.2926 -2.1859 -2.1422 -1.9624 -1.9223 -1.8666
## 261 254 96 212 205 167 13 136 5 12
## -1.8236 -1.7219 -1.6875 -1.6067 -1.5015 -1.4685 -1.4274 -1.4261 -1.4242 -1.4194
## 98 317 343 141 312 230 354 105 255 64
## -1.4193 -1.3920 -1.3672 -1.3369 -1.3199 -1.2969 -1.2716 -1.1897 -1.1793 -1.1651
## 118 342 355 178 245 323 198 51 256 172
## -1.1608 -1.1510 -1.1330 -1.1274 -1.0526 -1.0435 -1.0185 -1.0158 -1.0099 -1.0085
## 77 151 42 232 226 242 154 72 260 79
## -0.9825 -0.9661 -0.9502 -0.9394 -0.9164 -0.9147 -0.9090 -0.9089 -0.8912 -0.8831
## 162 69 339 112 258 335 359 108 210 220
## -0.8800 -0.8721 -0.8699 -0.8352 -0.8238 -0.8070 -0.7879 -0.7863 -0.7774 -0.7715
## 270 4 249 53 303 351 310 131 211 327
## -0.7680 -0.7673 -0.7499 -0.7491 -0.7320 -0.7104 -0.7089 -0.7011 -0.6672 -0.6628
## 117 290 43 221 170 239 25 80 6 213
## -0.6407 -0.6367 -0.6351 -0.6091 -0.5970 -0.5858 -0.5854 -0.5811 -0.5694 -0.5657
## 223 197 302 299 38 194 164 301 294 233
## -0.5643 -0.5625 -0.5620 -0.5429 -0.5390 -0.5341 -0.5282 -0.5248 -0.5221 -0.5209
## 219 143 243 33 275 329 128 196 322 132
## -0.5187 -0.5178 -0.4959 -0.4816 -0.4811 -0.4734 -0.4632 -0.4575 -0.4574 -0.4510
## 321 60 83 130 307 168 344 150 122 127
## -0.4486 -0.4448 -0.4441 -0.4392 -0.4234 -0.4223 -0.4193 -0.4188 -0.4163 -0.4018
## 346 92 201 169 349 216 280 3 126 68
## -0.3960 -0.3950 -0.3939 -0.3938 -0.3899 -0.3892 -0.3846 -0.3816 -0.3774 -0.3729
## 133 179 123 247 326 353 90 234 189 206
## -0.3689 -0.3644 -0.3609 -0.3582 -0.3548 -0.3479 -0.3387 -0.3365 -0.3356 -0.3216
## 251 2 110 330 314 182 28 158 246 207
## -0.3169 -0.3153 -0.3147 -0.3006 -0.2888 -0.2880 -0.2804 -0.2794 -0.2731 -0.2702
## 276 121 285 227 63 304 257 278 236 61
## -0.2682 -0.2520 -0.2496 -0.2494 -0.2420 -0.2417 -0.2400 -0.2335 -0.2235 -0.2161
## 46 8 316 263 308 135 19 106 333 175
## -0.2117 -0.2073 -0.2073 -0.1991 -0.1968 -0.1947 -0.1943 -0.1940 -0.1928 -0.1893
## 73 75 298 149 37 195 50 17 81 292
## -0.1830 -0.1583 -0.1556 -0.1523 -0.1499 -0.1499 -0.1487 -0.1478 -0.1461 -0.1453
## 324 250 29 305 202 295 18 87 134 159
## -0.1375 -0.1235 -0.1234 -0.1208 -0.1196 -0.1092 -0.1091 -0.1085 -0.1041 -0.1026
## 337 16 289 311 208 191 49 183 58 225
## -0.1004 -0.0985 -0.0964 -0.0959 -0.0935 -0.0933 -0.0928 -0.0918 -0.0798 -0.0702
## 181 148 199 7 274 27 78 94 32 173
## -0.0628 -0.0608 -0.0608 -0.0568 -0.0536 -0.0519 -0.0515 -0.0466 -0.0443 -0.0439
## 296 144 95 174 352 138 345 334 142 40
## -0.0432 -0.0418 -0.0342 -0.0338 -0.0300 -0.0270 -0.0227 -0.0213 -0.0168 -0.0060
## 155 119 177 336 265 287 145 62 21 111
## -0.0038 -0.0034 0.0026 0.0244 0.0255 0.0281 0.0413 0.0507 0.0576 0.0615
## 129 15 76 203 113 340 267 85 11 348
## 0.0626 0.0655 0.0710 0.0738 0.0869 0.0892 0.0933 0.0941 0.1051 0.1099
## 30 338 152 204 328 39 26 23 101 48
## 0.1123 0.1140 0.1235 0.1366 0.1507 0.1509 0.1533 0.1568 0.1764 0.1838
## 103 224 88 120 146 114 306 116 288 82
## 0.1987 0.1987 0.2082 0.2089 0.2151 0.2186 0.2192 0.2234 0.2272 0.2328
## 84 35 347 209 1 67 331 252 71 313
## 0.2355 0.2359 0.2394 0.2425 0.2454 0.2488 0.2516 0.2602 0.2696 0.2713
## 86 222 115 93 45 156 184 56 235 104
## 0.2736 0.2777 0.2878 0.2914 0.2942 0.2952 0.2992 0.3305 0.3360 0.3483
## 91 54 124 57 74 70 89 192 214 248
## 0.3525 0.3632 0.3783 0.4117 0.4120 0.4452 0.4592 0.4916 0.4946 0.5117
## 253 357 100 97 262 65 190 44 66 272
## 0.5264 0.5315 0.5888 0.5966 0.5971 0.5996 0.6103 0.6227 0.6239 0.6452
## 283 160 318 297 20 41 268 341 217 200
## 0.6506 0.6662 0.6705 0.6848 0.6930 0.7401 0.7554 0.7700 0.7970 0.8386
## 107 147 165 315 9 171 269 286 356 55
## 0.8594 0.8753 0.8754 0.8965 0.9012 0.9074 0.9563 0.9813 0.9951 1.0150
## 320 332 241 157 266 293 244 59 161 31
## 1.0161 1.0190 1.0648 1.0792 1.1018 1.1161 1.1476 1.1532 1.1618 1.1715
## 125 185 102 284 140 14 163 180 350 237
## 1.1803 1.1862 1.2254 1.2589 1.2804 1.3054 1.3260 1.3260 1.3665 1.4010
## 187 279 238 10 240 215 309 109 22 218
## 1.4109 1.4552 1.5377 1.5632 1.5840 1.6184 1.6506 1.6629 1.7109 1.7365
## 24 99 231 176 229 139 264 319 228 325
## 1.7658 1.7988 1.8000 1.9102 1.9859 2.0447 2.0734 2.3491 2.4783 2.5860
## 281 271 300 186 358 259 137 47
## 2.8653 2.8803 3.1241 3.2123 3.6390 3.6724 4.0198 5.0523
jackknife_outliers2 <- NHL %>% filter(jackknife2 > t2 | jackknife2 < -t2)
jackknife_outliers2
## # A tibble: 35 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 5000000 87-01… St. … MB CAN CAN 72 196 2005 5 132 L
## 2 7000000 85-12… Queb… QC CAN USA 72 202 2005 2 44 L
## 3 925000 96-10… Nort… MA USA USA 74 196 2015 1 2 R
## 4 832500 95-04… Lond… ON CAN CAN 72 223 2013 1 9 L
## 5 13800000 88-04… Winn… MB CAN CAN 74 201 2006 1 3 L
## 6 875000 93-02… Vict… QC CAN CAN 73 193 2011 1 26 L
## 7 6500000 84-03… Winn… MB CAN SWE 72 211 2002 1 24 L
## 8 3650000 89-10… Edmo… AB CAN CAN 69 175 2008 1 26 L
## 9 13800000 88-11… Buff… NY USA USA 71 177 2007 1 1 L
## 10 9000000 87-10… Madi… WI USA USA 72 202 2006 1 5 R
## # ℹ 25 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
cookCV2 <- 4/359
cookCV2
## [1] 0.01114206
cook2 <- cooks.distance(model2)
sort(round(cook2, 4))
## 7 11 15 16 18 21 26 27 29 30 32
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 37 40 49 50 58 62 76 78 81 85 87
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 94 95 111 113 119 129 134 138 142 144 145
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 148 149 152 155 159 173 174 175 177 181 183
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 191 195 199 202 203 204 208 225 250 265 267
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 274 287 289 295 296 334 336 337 338 340 345
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 348 352 1 8 17 19 23 35 39 46 48
## 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 61 63 71 73 75 82 84 86 101 146 156
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 158 182 184 189 207 209 216 222 224 227 234
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 235 236 247 251 252 257 263 292 298 305 311
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 324 328 333 347 2 28 45 67 68 88 93
## 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
## 106 120 135 150 169 179 196 197 201 206 214
## 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
## 243 246 253 276 278 285 288 304 306 308 316
## 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
## 331 54 56 91 103 114 116 121 164 168 194
## 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
## 213 223 313 330 353 74 83 89 90 123 124
## 0.0003 0.0003 0.0003 0.0003 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004
## 239 248 262 280 314 326 3 57 92 115 133
## 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005 0.0005 0.0005
## 190 211 268 270 329 38 60 110 126 127 249
## 0.0005 0.0005 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006
## 272 346 80 97 104 130 160 217 233 260 344
## 0.0006 0.0006 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007
## 349 33 43 65 122 132 154 198 226 301 307
## 0.0007 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008
## 70 128 165 221 258 275 299 44 53 357 6
## 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0010 0.0010 0.0010 0.0011
## 20 100 143 147 192 294 256 321 25 66 172
## 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0012 0.0012 0.0013 0.0013 0.0013
## 178 200 210 245 290 322 170 242 283 9 151
## 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 0.0014 0.0014 0.0014 0.0015 0.0015
## 161 171 241 327 335 79 180 219 220 351 185
## 0.0015 0.0015 0.0015 0.0015 0.0015 0.0016 0.0016 0.0016 0.0016 0.0016 0.0017
## 297 302 4 51 72 162 255 341 303 359 232
## 0.0017 0.0017 0.0018 0.0018 0.0018 0.0018 0.0018 0.0018 0.0019 0.0019 0.0021
## 269 310 318 41 266 117 69 131 187 42 157
## 0.0021 0.0021 0.0021 0.0022 0.0022 0.0024 0.0025 0.0025 0.0025 0.0026 0.0027
## 64 332 14 244 31 264 342 102 238 108 286
## 0.0028 0.0028 0.0030 0.0030 0.0031 0.0031 0.0031 0.0032 0.0032 0.0033 0.0033
## 55 230 261 293 339 77 355 356 112 320 218
## 0.0034 0.0036 0.0036 0.0036 0.0036 0.0038 0.0038 0.0038 0.0039 0.0040 0.0041
## 5 107 176 240 22 212 237 125 167 354 231
## 0.0043 0.0043 0.0043 0.0043 0.0044 0.0044 0.0045 0.0047 0.0047 0.0048 0.0049
## 205 118 323 24 343 96 315 12 215 13 163
## 0.0050 0.0051 0.0051 0.0052 0.0052 0.0053 0.0054 0.0055 0.0055 0.0056 0.0056
## 350 228 141 279 284 312 166 99 140 229 153
## 0.0066 0.0067 0.0070 0.0071 0.0072 0.0072 0.0079 0.0080 0.0080 0.0084 0.0085
## 59 254 136 273 98 105 309 10 188 139 317
## 0.0087 0.0092 0.0100 0.0106 0.0111 0.0119 0.0120 0.0128 0.0129 0.0134 0.0134
## 36 34 193 109 282 186 325 277 291 319 281
## 0.0139 0.0151 0.0152 0.0158 0.0180 0.0190 0.0191 0.0199 0.0207 0.0218 0.0245
## 271 300 259 358 47 137
## 0.0248 0.0296 0.0317 0.0344 0.0622 0.0836
cook_outliers2 <- NHL %>% filter(cook2 > cookCV2)
cook_outliers2
## # A tibble: 23 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 10900000 87-08… Cole… NS CAN CAN 71 200 2005 1 1 L
## 2 925000 96-10… Nort… MA USA USA 74 196 2015 1 2 R
## 3 832500 95-04… Lond… ON CAN CAN 72 223 2013 1 9 L
## 4 13800000 88-04… Winn… MB CAN CAN 74 201 2006 1 3 L
## 5 1300000 89-04… Otta… ON CAN CAN 69 160 2007 6 179 L
## 6 3650000 89-10… Edmo… AB CAN CAN 69 175 2008 1 26 L
## 7 13800000 88-11… Buff… NY USA USA 71 177 2007 1 1 L
## 8 9000000 87-10… Madi… WI USA USA 72 202 2006 1 5 R
## 9 11000000 89-05… Toro… ON CAN CAN 72 210 2007 2 43 R
## 10 925000 97-07… Gros… MI USA USA 74 218 2015 1 8 L
## # ℹ 13 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
ggplot(NHL, aes(x = fitted(model2), y = jackknife2)) + geom_point()+ geom_hline(yintercept = t2, col = "purple") + geom_hline(yintercept = -t2, col = "purple")
## Warning: Removed 1 rows containing missing values (`geom_point()`).
qqnorm(resid(model2))
qqline(resid(model2), col = "red", lwd = 2)
qqPlot(resid(model2))
## [1] 47 137
skewness(jackknife2)
## [1] NaN
kurtosis(jackknife2)
## [1] NaN
ols_vif_tol(model2)
## Variables Tolerance VIF
## 1 GS 0.3687451 2.711900
## 2 Wt 0.7929157 1.261168
## 3 iHDf 0.7352171 1.360143
## 4 GP 0.4179533 2.392612
## 5 PM 0.8535418 1.171589
## 6 Position_CD 0.9734760 1.027247
## 7 Position_CLW 0.5769079 1.733379
## 8 Position_CRW 0.6918443 1.445412
## 9 Position_CLWRW 0.7925824 1.261698
## 10 Position_D 0.4184927 2.389528
## 11 Position_LW 0.6632397 1.507751
## 12 Position_LWRW 0.7268771 1.375748
## 13 Position_RW 0.6428804 1.555499
eigprop(model2)
##
## Call:
## eigprop(mod = model2)
##
## Eigenvalues CI (Intercept) GS Wt iHDf GP PM
## 1 4.3967 1.0000 0.0002 0.0064 0.0002 0.0008 0.0044 0.0000
## 2 1.3557 1.8009 0.0000 0.0060 0.0000 0.1987 0.0001 0.1924
## 3 1.0658 2.0311 0.0000 0.0002 0.0000 0.0432 0.0000 0.1262
## 4 1.0206 2.0755 0.0000 0.0038 0.0000 0.0025 0.0001 0.0042
## 5 1.0031 2.0936 0.0000 0.0001 0.0000 0.0000 0.0002 0.0000
## 6 1.0001 2.0968 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 7 1.0000 2.0968 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 8 1.0000 2.0968 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 9 0.8984 2.2122 0.0000 0.0073 0.0000 0.0061 0.0001 0.2520
## 10 0.7520 2.4179 0.0000 0.0006 0.0000 0.4934 0.0000 0.2288
## 11 0.3469 3.5603 0.0010 0.2285 0.0009 0.0542 0.0315 0.1442
## 12 0.0940 6.8390 0.0076 0.0679 0.0072 0.0023 0.0161 0.0185
## 13 0.0645 8.2551 0.0028 0.6784 0.0027 0.0879 0.9470 0.0315
## 14 0.0022 44.6381 0.9883 0.0009 0.9890 0.1110 0.0004 0.0021
## Position_CD Position_CLW Position_CRW Position_CLWRW Position_D Position_LW
## 1 0.0000 0.0039 0.0028 0.0020 0.0047 0.0025
## 2 0.0001 0.0019 0.0003 0.0004 0.0072 0.0681
## 3 0.0001 0.1669 0.0021 0.0355 0.0081 0.0002
## 4 0.1030 0.0001 0.1955 0.0843 0.0710 0.0358
## 5 0.2362 0.0044 0.2253 0.0201 0.0029 0.0547
## 6 0.3994 0.0411 0.0746 0.0504 0.0242 0.0239
## 7 0.0433 0.0263 0.0383 0.3753 0.0003 0.0689
## 8 0.1775 0.1080 0.0138 0.1297 0.0096 0.0202
## 9 0.0044 0.0008 0.0157 0.0023 0.0409 0.2484
## 10 0.0003 0.0611 0.0002 0.0084 0.0027 0.0362
## 11 0.0046 0.0731 0.0759 0.0632 0.0143 0.0343
## 12 0.0205 0.5006 0.3089 0.2141 0.8053 0.3891
## 13 0.0061 0.0005 0.0411 0.0012 0.0001 0.0158
## 14 0.0045 0.0113 0.0053 0.0130 0.0087 0.0019
## Position_LWRW Position_RW
## 1 0.0024 0.0029
## 2 0.0366 0.0015
## 3 0.0018 0.1794
## 4 0.0215 0.0361
## 5 0.1792 0.0001
## 6 0.0003 0.1119
## 7 0.1577 0.0019
## 8 0.1106 0.1025
## 9 0.0813 0.0252
## 10 0.0377 0.0644
## 11 0.0616 0.0224
## 12 0.3090 0.4437
## 13 0.0000 0.0082
## 14 0.0001 0.0000
##
## ===============================
## Row 13==> GS, proportion 0.678401 >= 0.50
## Row 14==> Wt, proportion 0.988967 >= 0.50
## Row 13==> GP, proportion 0.947009 >= 0.50
## Row 12==> Position_CLW, proportion 0.500612 >= 0.50
## Row 12==> Position_D, proportion 0.805286 >= 0.50
ols_step_forward_p(model2)
##
## Selection Summary
## -------------------------------------------------------------------------------------
## Variable Adj.
## Step Entered R-Square R-Square C(p) AIC RMSE
## -------------------------------------------------------------------------------------
## 1 GS 0.4540 0.4525 23.0936 11365.1352 1801945.3109
## 2 Wt 0.4811 0.4781 6.3504 11348.8823 1759179.4048
## 3 Position_CLW 0.4889 0.4846 2.9042 11345.3998 1748254.9274
## 4 Position_RW 0.4922 0.4865 2.6132 11345.0682 1745046.4442
## 5 iHDf 0.4941 0.4870 3.2952 11345.7201 1744238.3455
## 6 GP 0.4965 0.4879 3.6417 11346.0214 1742586.7942
## 7 PM 0.4983 0.4883 4.3927 11346.7329 1741938.5202
## 8 Position_D 0.5002 0.4888 5.0960 11347.3904 1741166.5170
## -------------------------------------------------------------------------------------
ols_step_backward_p(model2)
##
##
## Elimination Summary
## ---------------------------------------------------------------------------------------
## Variable Adj.
## Step Removed R-Square R-Square C(p) AIC RMSE
## ---------------------------------------------------------------------------------------
## 1 Position_LWRW 0.5018 0.4845 12.0164 11354.2689 1748468.8164
## 2 Position_CD 0.5017 0.4859 10.0756 11352.3304 1746097.3016
## 3 Position_CRW 0.5015 0.4872 8.1601 11350.4184 1743800.3113
## 4 Position_LW 0.5013 0.4885 6.3204 11348.5850 1741704.3497
## 5 Position_CLWRW 0.5002 0.4888 5.0960 11347.3904 1741166.5170
## ---------------------------------------------------------------------------------------
ols_step_both_p(model2)
##
## Stepwise Selection Summary
## -------------------------------------------------------------------------------------------------
## Added/ Adj.
## Step Variable Removed R-Square R-Square C(p) AIC RMSE
## -------------------------------------------------------------------------------------------------
## 1 GS addition 0.454 0.452 23.0940 11365.1352 1801945.3109
## 2 Wt addition 0.481 0.478 6.3500 11348.8823 1759179.4048
## 3 Position_CLW addition 0.489 0.485 2.9040 11345.3998 1748254.9274
## -------------------------------------------------------------------------------------------------
model3 <- lm(Salary ~ GS + Wt + Position_CD + Position_CLW + Position_CRW + Position_CLWRW + Position_D + Position_LW + Position_LWRW + Position_RW, data = NHL)
model3
##
## Call:
## lm(formula = Salary ~ GS + Wt + Position_CD + Position_CLW +
## Position_CRW + Position_CLWRW + Position_D + Position_LW +
## Position_LWRW + Position_RW, data = NHL)
##
## Coefficients:
## (Intercept) GS Wt Position_CD Position_CLW
## -4008930 76227 23787 573275 -619389
## Position_CRW Position_CLWRW Position_D Position_LW Position_LWRW
## 235044 -390007 136463 -14554 75323
## Position_RW
## -402641
standard_error3 <- sqrt(deviance(model3)/df.residual(model3))
standard_error3
## [1] 1755832
2*standard_error3
## [1] 3511665
plot(fitted(model3),resid(model3))
abline(h=2*standard_error3, col = "blue")
abline(h=-2*standard_error3, col = "blue")
abline(h=3*standard_error3, col = "red")
abline(h=-3*standard_error3, col = "red")
res_pot_outliers3 <- NHL %>% filter(2*standard_error3 <= abs(resid(model3)) & abs(resid(model3)) < 3*standard_error3)
print(res_pot_outliers3)
## # A tibble: 13 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 925000 96-10-… Nort… MA USA USA 74 196 2015 1 2 R
## 2 832500 95-04-… Lond… ON CAN CAN 72 223 2013 1 9 L
## 3 742500 94-05-… Denv… CO USA USA 74 205 2012 4 120 L
## 4 925000 97-07-… Gros… MI USA USA 74 218 2015 1 8 L
## 5 7500000 85-04-… Edmo… AB CAN CAN 75 219 2003 1 9 L
## 6 6000000 83-03-… Kitc… ON CAN CAN 72 202 2002 8 241 R
## 7 9000000 85-01-… Madi… WI USA USA 74 206 2003 1 7 L
## 8 925000 93-05-… St. … AB CAN CAN 78 226 2012 3 86 R
## 9 925000 97-12-… Scot… AZ USA USA 74 202 2016 1 6 L
## 10 9000000 84-07-… Minn… MN USA USA 71 196 2003 1 17 L
## 11 832500 95-03-… Ste-… QC CAN CAN 71 188 2013 1 3 L
## 12 8000000 84-06-… Bram… ON CAN CAN 76 212 2002 1 1 L
## 13 8000000 88-04-… St. … MN USA USA 72 218 2006 1 7 R
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, iCF...42 <dbl>,
## # iFF <dbl>, iSF...44 <dbl>, iSF...45 <dbl>, iSF...46 <dbl>, ixG <dbl>, …
res_outliers3 <- NHL %>% filter(abs(resid(model3)) >= 3*standard_error3)
print(res_outliers3)
## # A tibble: 6 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 13800000 88-04-… Winn… MB CAN CAN 74 201 2006 1 3 L
## 2 13800000 88-11-… Buff… NY USA USA 71 177 2007 1 1 L
## 3 11000000 89-05-… Toro… ON CAN CAN 72 210 2007 2 43 R
## 4 12000000 85-08-… Sica… BC CAN CAN 76 232 2003 2 49 R
## 5 8000000 85-12-… Mapl… BC CAN CAN 75 200 2004 1 4 L
## 6 6500000 85-03-… Roch… NY USA USA 70 187 2004 4 127 R
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, iCF...42 <dbl>,
## # iFF <dbl>, iSF...44 <dbl>, iSF...45 <dbl>, iSF...46 <dbl>, ixG <dbl>, …
h3 <- 2*(3+1)/359
h3
## [1] 0.02228412
leverage3 <- hatvalues(model3)
sort(round(leverage3,4))
## 215 226 232 241 252 197 264 146 151 225 247
## 0.0078 0.0078 0.0078 0.0078 0.0078 0.0079 0.0079 0.0080 0.0080 0.0080 0.0080
## 256 213 198 249 254 238 164 174 194 231 211
## 0.0081 0.0082 0.0083 0.0083 0.0083 0.0084 0.0085 0.0085 0.0085 0.0086 0.0087
## 180 184 196 243 272 209 237 250 169 217 185
## 0.0088 0.0088 0.0088 0.0088 0.0088 0.0089 0.0089 0.0089 0.0090 0.0090 0.0091
## 253 270 167 230 214 260 223 191 201 234 255
## 0.0091 0.0091 0.0093 0.0093 0.0094 0.0094 0.0096 0.0097 0.0098 0.0098 0.0098
## 207 216 183 150 176 189 236 251 263 148 166
## 0.0099 0.0099 0.0100 0.0101 0.0101 0.0101 0.0101 0.0101 0.0101 0.0103 0.0103
## 228 261 257 179 163 165 178 258 268 168 205
## 0.0103 0.0103 0.0105 0.0106 0.0107 0.0107 0.0107 0.0107 0.0107 0.0108 0.0108
## 227 245 156 204 219 229 233 190 208 154 175
## 0.0108 0.0108 0.0110 0.0110 0.0110 0.0110 0.0111 0.0113 0.0113 0.0114 0.0114
## 173 239 271 222 147 155 182 262 195 202 153
## 0.0115 0.0115 0.0115 0.0116 0.0118 0.0118 0.0118 0.0119 0.0120 0.0120 0.0122
## 160 159 187 172 145 152 242 161 235 149 269
## 0.0123 0.0129 0.0129 0.0130 0.0133 0.0133 0.0136 0.0137 0.0139 0.0140 0.0140
## 220 162 186 218 248 199 206 240 265 246 212
## 0.0144 0.0146 0.0147 0.0148 0.0150 0.0151 0.0152 0.0152 0.0154 0.0156 0.0158
## 266 158 181 244 203 170 273 200 188 51 20
## 0.0158 0.0161 0.0164 0.0165 0.0166 0.0173 0.0173 0.0179 0.0189 0.0197 0.0198
## 22 5 79 73 38 43 44 69 14 83 3
## 0.0198 0.0199 0.0200 0.0201 0.0203 0.0207 0.0207 0.0207 0.0208 0.0208 0.0210
## 68 28 40 75 210 94 58 62 4 24 2
## 0.0210 0.0212 0.0212 0.0213 0.0213 0.0214 0.0215 0.0215 0.0216 0.0218 0.0219
## 63 7 224 46 88 171 8 53 49 86 193
## 0.0219 0.0220 0.0220 0.0221 0.0221 0.0221 0.0222 0.0224 0.0225 0.0226 0.0226
## 37 39 95 29 85 60 221 27 55 21 78
## 0.0227 0.0227 0.0227 0.0228 0.0229 0.0231 0.0231 0.0232 0.0232 0.0233 0.0233
## 15 26 32 89 267 67 56 72 259 64 18
## 0.0234 0.0234 0.0234 0.0234 0.0234 0.0235 0.0237 0.0239 0.0239 0.0240 0.0241
## 96 16 66 74 99 9 71 30 48 93 70
## 0.0241 0.0242 0.0242 0.0243 0.0245 0.0246 0.0246 0.0247 0.0248 0.0248 0.0249
## 11 35 42 61 97 17 157 34 50 19 84
## 0.0250 0.0250 0.0250 0.0250 0.0250 0.0251 0.0252 0.0253 0.0253 0.0255 0.0255
## 87 80 177 65 1 45 59 100 101 81 102
## 0.0255 0.0264 0.0267 0.0271 0.0274 0.0275 0.0275 0.0280 0.0282 0.0284 0.0286
## 335 347 344 351 47 353 91 54 31 82 350
## 0.0286 0.0286 0.0287 0.0289 0.0292 0.0292 0.0293 0.0294 0.0296 0.0298 0.0305
## 333 336 326 343 36 329 342 357 328 348 23
## 0.0309 0.0309 0.0310 0.0310 0.0311 0.0313 0.0313 0.0313 0.0315 0.0316 0.0319
## 92 340 76 332 338 352 12 325 345 355 331
## 0.0319 0.0319 0.0320 0.0321 0.0322 0.0324 0.0326 0.0326 0.0326 0.0327 0.0330
## 303 330 57 279 294 290 300 301 25 358 276
## 0.0333 0.0334 0.0336 0.0336 0.0336 0.0338 0.0343 0.0344 0.0345 0.0346 0.0347
## 293 280 295 298 354 285 349 289 274 334 286
## 0.0352 0.0353 0.0354 0.0356 0.0356 0.0357 0.0357 0.0358 0.0360 0.0361 0.0364
## 13 283 287 275 118 296 356 359 192 297 341
## 0.0365 0.0365 0.0367 0.0370 0.0373 0.0377 0.0378 0.0378 0.0380 0.0385 0.0386
## 6 124 288 135 346 302 281 299 90 337 278
## 0.0387 0.0388 0.0389 0.0392 0.0392 0.0394 0.0396 0.0399 0.0401 0.0403 0.0408
## 127 128 33 133 123 132 139 277 125 282 142
## 0.0409 0.0409 0.0412 0.0412 0.0413 0.0420 0.0420 0.0426 0.0428 0.0429 0.0430
## 119 141 138 292 41 327 134 291 140 126 312
## 0.0433 0.0442 0.0443 0.0444 0.0453 0.0453 0.0455 0.0458 0.0463 0.0472 0.0478
## 316 131 144 318 320 136 143 122 319 130 309
## 0.0478 0.0484 0.0484 0.0487 0.0487 0.0489 0.0490 0.0492 0.0497 0.0501 0.0503
## 129 284 304 10 310 305 314 77 315 121 308
## 0.0506 0.0508 0.0508 0.0510 0.0510 0.0512 0.0512 0.0516 0.0525 0.0533 0.0546
## 339 307 98 313 120 317 322 306 311 323 324
## 0.0551 0.0554 0.0562 0.0569 0.0577 0.0584 0.0589 0.0592 0.0592 0.0601 0.0637
## 137 321 112 108 113 107 110 116 114 104 109
## 0.0640 0.0651 0.0673 0.0676 0.0685 0.0695 0.0698 0.0700 0.0706 0.0725 0.0732
## 115 117 111 103 106 105 52
## 0.0732 0.0738 0.0767 0.0778 0.0790 0.0851 1.0000
leverage_outliers3 <- NHL %>% filter(leverage3 > h3)
leverage_outliers3
## # A tibble: 209 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 925000 93-04… Peta… ON CAN CAN 68 178 2011 7 201 L
## 2 6000000 90-09… Miss… ON CAN CAN 73 211 2009 1 1 L
## 3 3500000 80-02… Mont… QC CAN CAN 72 179 1998 2 45 L
## 4 10900000 87-08… Cole… NS CAN CAN 71 200 2005 1 1 L
## 5 667500 97-01… Saul… ON CAN CAN 71 185 2015 3 67 R
## 6 3500000 84-10… Thun… ON CAN CAN 76 208 2003 1 2 L
## 7 667500 96-03… Calg… AB CAN CAN 70 166 2014 3 79 R
## 8 700000 90-12… Vaug… ON CAN CAN 70 193 2009 5 147 L
## 9 3750000 92-12… Phoe… AZ USA CAN 75 211 2011 1 8 L
## 10 600000 93-04… Bram… ON CAN CAN 77 212 2011 7 191 L
## # ℹ 199 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
t3 <- qt(df = 359 - 3 - 2, 0.95)
t3
## [1] 1.649169
jackknife3 <- rstudent(model3)
sort(round(jackknife3, 4))
## 188 277 273 36 153 34 291 193 261 282
## -2.8239 -2.4769 -2.3533 -2.3156 -2.1929 -2.1856 -2.1652 -1.8611 -1.8173 -1.8066
## 205 96 166 317 230 141 254 12 13 167
## -1.7870 -1.7557 -1.6566 -1.5788 -1.5405 -1.4934 -1.4847 -1.4768 -1.4687 -1.4313
## 212 354 343 98 5 312 355 151 255 105
## -1.4263 -1.3779 -1.3751 -1.3139 -1.2996 -1.2331 -1.2283 -1.2140 -1.1930 -1.1929
## 342 118 64 136 51 323 198 245 42 77
## -1.1787 -1.1634 -1.1550 -1.1530 -1.1168 -1.0909 -1.0900 -1.0862 -1.0354 -1.0158
## 178 226 112 172 232 256 260 258 154 72
## -1.0095 -0.9849 -0.9847 -0.9505 -0.9438 -0.9354 -0.9120 -0.9008 -0.8740 -0.8651
## 303 233 249 53 359 335 210 270 108 294
## -0.8553 -0.8494 -0.8372 -0.8009 -0.7924 -0.7860 -0.7838 -0.7798 -0.7674 -0.7606
## 69 25 43 339 128 310 213 242 79 117
## -0.7601 -0.7599 -0.7522 -0.7520 -0.7254 -0.7234 -0.7217 -0.7185 -0.7099 -0.7025
## 162 321 239 290 4 327 351 211 38 80
## -0.6988 -0.6790 -0.6583 -0.6551 -0.6541 -0.6528 -0.6488 -0.6213 -0.6188 -0.6179
## 346 307 83 220 33 329 127 143 299 221
## -0.5999 -0.5760 -0.5750 -0.5735 -0.5634 -0.5485 -0.5477 -0.5351 -0.5290 -0.5287
## 197 164 246 330 223 243 234 194 6 135
## -0.5024 -0.4997 -0.4860 -0.4763 -0.4744 -0.4702 -0.4664 -0.4654 -0.4617 -0.4613
## 148 353 123 133 131 170 302 68 28 301
## -0.4461 -0.4325 -0.4249 -0.4137 -0.4129 -0.4129 -0.4092 -0.4088 -0.4065 -0.4037
## 126 216 247 275 2 326 130 75 61 158
## -0.3954 -0.3916 -0.3906 -0.3904 -0.3900 -0.3825 -0.3696 -0.3611 -0.3593 -0.3574
## 92 169 132 150 196 349 276 17 94 344
## -0.3570 -0.3501 -0.3442 -0.3425 -0.3423 -0.3391 -0.3389 -0.3378 -0.3310 -0.3275
## 110 168 202 280 63 16 304 201 227 333
## -0.3256 -0.3186 -0.3105 -0.3073 -0.3055 -0.2965 -0.2898 -0.2880 -0.2824 -0.2722
## 278 179 314 106 285 324 250 122 189 19
## -0.2721 -0.2705 -0.2704 -0.2581 -0.2543 -0.2503 -0.2461 -0.2432 -0.2351 -0.2338
## 73 46 219 251 311 90 3 191 207 142
## -0.2326 -0.2304 -0.2211 -0.2178 -0.2077 -0.2008 -0.1972 -0.1799 -0.1787 -0.1783
## 206 182 8 134 60 88 81 236 298 195
## -0.1734 -0.1707 -0.1682 -0.1682 -0.1576 -0.1542 -0.1529 -0.1388 -0.1306 -0.1280
## 322 50 257 121 62 144 295 337 87 352
## -0.1258 -0.1238 -0.1204 -0.1192 -0.1123 -0.1085 -0.1044 -0.1041 -0.1029 -0.0979
## 175 208 29 289 37 18 49 316 305 263
## -0.0967 -0.0961 -0.0940 -0.0912 -0.0900 -0.0894 -0.0881 -0.0865 -0.0794 -0.0790
## 78 149 58 174 274 296 225 308 183 119
## -0.0722 -0.0712 -0.0681 -0.0609 -0.0502 -0.0422 -0.0406 -0.0342 -0.0308 -0.0284
## 7 173 138 39 159 334 40 345 27 287
## -0.0222 -0.0170 -0.0127 -0.0065 -0.0032 0.0059 0.0103 0.0141 0.0184 0.0200
## 32 336 292 199 23 95 203 181 146 85
## 0.0321 0.0352 0.0392 0.0531 0.0568 0.0608 0.0652 0.0667 0.0707 0.0782
## 265 129 101 155 222 21 76 15 328 111
## 0.0791 0.0869 0.1006 0.1046 0.1108 0.1162 0.1198 0.1206 0.1305 0.1313
## 116 340 348 177 48 113 11 184 204 82
## 0.1518 0.1520 0.1537 0.1580 0.1636 0.1659 0.1676 0.1698 0.1724 0.1762
## 145 338 30 267 26 91 84 224 288 103
## 0.1766 0.1898 0.1901 0.2150 0.2209 0.2213 0.2239 0.2347 0.2395 0.2405
## 313 192 120 209 347 86 252 114 306 331
## 0.2431 0.2466 0.2542 0.2801 0.2845 0.2862 0.2914 0.2929 0.2981 0.3000
## 1 45 35 71 54 235 156 56 93 115
## 0.3113 0.3201 0.3204 0.3333 0.3356 0.3453 0.3504 0.3514 0.3584 0.3634
## 67 89 214 152 104 272 190 124 297 262
## 0.3636 0.3723 0.3996 0.4087 0.4193 0.4393 0.4576 0.4688 0.4855 0.4865
## 248 74 66 253 283 20 57 70 97 217
## 0.4948 0.4982 0.5283 0.5303 0.5384 0.5475 0.5505 0.5573 0.6048 0.6239
## 100 357 65 341 44 200 269 268 318 160
## 0.6427 0.6506 0.6754 0.6820 0.6828 0.6829 0.6890 0.7167 0.7290 0.7457
## 107 41 356 320 157 9 165 147 315 185
## 0.7784 0.8497 0.9143 0.9208 0.9329 0.9471 0.9485 0.9679 0.9752 0.9849
## 266 171 293 286 241 31 163 332 244 102
## 1.0048 1.0135 1.0284 1.0861 1.0912 1.1062 1.1097 1.1415 1.1464 1.1943
## 125 161 279 14 180 55 59 215 237 284
## 1.2159 1.2457 1.2463 1.2782 1.2808 1.3006 1.3236 1.3771 1.4046 1.4365
## 140 350 187 238 99 240 229 109 10 22
## 1.4826 1.5026 1.5457 1.5703 1.6677 1.6722 1.6764 1.6857 1.7240 1.7292
## 218 309 24 231 139 176 264 319 228 325
## 1.7457 1.7708 1.7872 1.8810 1.9795 2.0066 2.0660 2.2848 2.4951 2.5806
## 271 281 300 186 259 358 137 47
## 2.6642 2.8455 3.1047 3.4088 3.6639 3.7158 3.9441 4.9392
jackknife_outliers3 <- NHL %>% filter(jackknife3 > t3 | jackknife3 < -t3)
jackknife_outliers3
## # A tibble: 37 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 10900000 87-08… Cole… NS CAN CAN 71 200 2005 1 1 L
## 2 5000000 87-01… St. … MB CAN CAN 72 196 2005 5 132 L
## 3 7000000 85-12… Queb… QC CAN USA 72 202 2005 2 44 L
## 4 925000 96-10… Nort… MA USA USA 74 196 2015 1 2 R
## 5 832500 95-04… Lond… ON CAN CAN 72 223 2013 1 9 L
## 6 13800000 88-04… Winn… MB CAN CAN 74 201 2006 1 3 L
## 7 875000 93-02… Vict… QC CAN CAN 73 193 2011 1 26 L
## 8 6500000 84-03… Winn… MB CAN SWE 72 211 2002 1 24 L
## 9 3650000 89-10… Edmo… AB CAN CAN 69 175 2008 1 26 L
## 10 13800000 88-11… Buff… NY USA USA 71 177 2007 1 1 L
## # ℹ 27 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
cookCV3 <- 4/359
cookCV3
## [1] 0.01114206
cook3 <- cooks.distance(model3)
sort(round(cook3, 4))
## 7 15 18 21 23 27 29 32 37 39 40
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 49 50 58 62 76 78 85 87 88 95 101
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 119 129 138 145 146 149 155 159 173 174 175
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 181 182 183 184 191 195 199 203 204 206 207
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 208 219 222 225 236 250 251 257 263 265 274
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 287 289 292 295 296 305 308 316 334 336 337
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 345 352 3 8 11 19 26 30 46 48 60
## 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 73 81 82 84 91 111 121 134 142 144 150
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 156 168 169 177 179 189 196 201 202 209 214
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 216 224 227 247 252 267 298 322 328 338 340
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 348 1 16 35 63 86 90 94 113 116 148
## 0.0001 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
## 152 158 164 190 192 194 197 223 234 235 243
## 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
## 253 272 285 288 311 333 347 2 17 28 45
## 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0003 0.0003 0.0003 0.0003
## 54 56 61 67 68 71 75 89 93 122 170
## 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
## 211 217 246 248 262 278 280 313 331 344 92
## 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0004
## 103 120 213 220 276 304 314 324 326 349 106
## 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005
## 132 239 249 268 270 275 301 306 353 20 66
## 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0006 0.0006
## 74 83 114 160 221 232 242 269 302 38 70
## 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007 0.0007
## 110 123 126 130 133 162 226 233 256 260 330
## 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007
## 6 124 131 135 154 185 200 258 4 44 79
## 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0009 0.0009 0.0009
## 80 97 165 198 241 297 329 57 115 147 178
## 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 0.0010 0.0010 0.0010 0.0010
## 283 43 69 100 151 172 299 351 33 65 127
## 0.0010 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0012 0.0012 0.0012
## 163 210 245 357 53 104 143 180 255 346 215
## 0.0012 0.0012 0.0012 0.0012 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 0.0014
## 290 266 237 72 167 254 335 341 294 307 327
## 0.0014 0.0015 0.0016 0.0017 0.0017 0.0017 0.0017 0.0017 0.0018 0.0018 0.0018
## 25 238 128 157 161 230 244 9 171 359 51
## 0.0019 0.0019 0.0020 0.0020 0.0020 0.0020 0.0020 0.0021 0.0021 0.0022 0.0023
## 303 42 318 166 310 187 229 231 321 64 212
## 0.0023 0.0025 0.0025 0.0026 0.0026 0.0028 0.0028 0.0028 0.0029 0.0030 0.0030
## 339 356 5 41 205 261 264 14 31 293 55
## 0.0030 0.0030 0.0031 0.0031 0.0031 0.0031 0.0031 0.0032 0.0034 0.0035 0.0036
## 117 176 102 108 240 320 332 107 218 286 342
## 0.0036 0.0037 0.0038 0.0039 0.0039 0.0039 0.0039 0.0041 0.0041 0.0041 0.0041
## 59 355 118 315 279 77 153 22 343 228 125
## 0.0045 0.0046 0.0048 0.0048 0.0049 0.0051 0.0054 0.0055 0.0055 0.0058 0.0060
## 136 99 24 112 350 354 12 96 312 323 193
## 0.0062 0.0063 0.0064 0.0064 0.0064 0.0064 0.0067 0.0069 0.0069 0.0069 0.0072
## 13 271 273 98 141 140 284 34 105 282 188
## 0.0074 0.0074 0.0088 0.0093 0.0093 0.0097 0.0100 0.0111 0.0120 0.0132 0.0137
## 317 10 309 186 36 139 325 291 109 277 319
## 0.0140 0.0145 0.0150 0.0153 0.0155 0.0155 0.0201 0.0202 0.0203 0.0245 0.0245
## 259 281 300 358 47 137
## 0.0289 0.0297 0.0304 0.0434 0.0626 0.0928
cook_outliers3 <- NHL %>% filter(cook3 > cookCV3)
cook_outliers3
## # A tibble: 20 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 10900000 87-08… Cole… NS CAN CAN 71 200 2005 1 1 L
## 2 832500 95-04… Lond… ON CAN CAN 72 223 2013 1 9 L
## 3 13800000 88-04… Winn… MB CAN CAN 74 201 2006 1 3 L
## 4 1300000 89-04… Otta… ON CAN CAN 69 160 2007 6 179 L
## 5 3650000 89-10… Edmo… AB CAN CAN 69 175 2008 1 26 L
## 6 13800000 88-11… Buff… NY USA USA 71 177 2007 1 1 L
## 7 9000000 87-10… Madi… WI USA USA 72 202 2006 1 5 R
## 8 11000000 89-05… Toro… ON CAN CAN 72 210 2007 2 43 R
## 9 925000 97-07… Gros… MI USA USA 74 218 2015 1 8 L
## 10 12000000 85-08… Sica… BC CAN CAN 76 232 2003 2 49 R
## 11 925000 97-12… Scot… AZ USA USA 74 202 2016 1 6 L
## 12 9000000 84-07… Minn… MN USA USA 71 196 2003 1 17 L
## 13 925000 95-12… Oran… ON CAN CAN 74 232 2014 1 10 L
## 14 832500 95-03… Ste-… QC CAN CAN 71 188 2013 1 3 L
## 15 8000000 85-12… Mapl… BC CAN CAN 75 200 2004 1 4 L
## 16 5500000 87-02… Musk… MI USA USA 74 218 2005 2 42 L
## 17 2000000 92-01… Newp… CA USA USA 71 187 2010 2 59 L
## 18 8000000 84-06… Bram… ON CAN CAN 76 212 2002 1 1 L
## 19 8000000 88-04… St. … MN USA USA 72 218 2006 1 7 R
## 20 6500000 85-03… Roch… NY USA USA 70 187 2004 4 127 R
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, iCF...42 <dbl>,
## # iFF <dbl>, iSF...44 <dbl>, iSF...45 <dbl>, iSF...46 <dbl>, ixG <dbl>, …
ggplot(NHL, aes(x = fitted(model3), y = jackknife3)) + geom_point()+ geom_hline(yintercept = t3, col = "purple") + geom_hline(yintercept = -t3, col = "purple")
## Warning: Removed 1 rows containing missing values (`geom_point()`).
qqnorm(resid(model3))
qqline(resid(model3), col = "red", lwd = 2)
qqPlot(resid(model3))
## [1] 47 137
skewness(jackknife3)
## [1] NaN
kurtosis(jackknife3)
## [1] NaN
ols_vif_tol(model3)
## Variables Tolerance VIF
## 1 GS 0.9614386 1.040108
## 2 Wt 0.9100763 1.098809
## 3 Position_CD 0.9777502 1.022756
## 4 Position_CLW 0.5847306 1.710189
## 5 Position_CRW 0.7006192 1.427309
## 6 Position_CLWRW 0.7998962 1.250162
## 7 Position_D 0.4282661 2.334997
## 8 Position_LW 0.6719400 1.488228
## 9 Position_LWRW 0.7442691 1.343600
## 10 Position_RW 0.6507281 1.536740
eigprop(model3)
##
## Call:
## eigprop(mod = model3)
##
## Eigenvalues CI (Intercept) GS Wt Position_CD Position_CLW
## 1 3.4957 1.0000 0.0004 0.0255 0.0004 0.0001 0.0063
## 2 1.0242 1.8475 0.0000 0.0128 0.0000 0.0609 0.0471
## 3 1.0001 1.8696 0.0000 0.0000 0.0000 0.4815 0.1409
## 4 1.0000 1.8697 0.0000 0.0000 0.0000 0.0143 0.0220
## 5 1.0000 1.8697 0.0000 0.0000 0.0000 0.0040 0.0001
## 6 1.0000 1.8697 0.0000 0.0000 0.0000 0.1403 0.1071
## 7 1.0000 1.8697 0.0000 0.0000 0.0000 0.0004 0.0534
## 8 1.0000 1.8697 0.0000 0.0000 0.0000 0.2684 0.0416
## 9 0.3833 3.0199 0.0006 0.9293 0.0006 0.0030 0.0486
## 10 0.0942 6.0912 0.0095 0.0325 0.0091 0.0225 0.5226
## 11 0.0025 37.2980 0.9895 0.0000 0.9899 0.0046 0.0102
## Position_CRW Position_CLWRW Position_D Position_LW Position_LWRW Position_RW
## 1 0.0049 0.0031 0.0080 0.0042 0.0036 0.0048
## 2 0.2018 0.1205 0.0666 0.0401 0.0008 0.0045
## 3 0.0432 0.0249 0.0029 0.0167 0.0612 0.0011
## 4 0.0001 0.0408 0.0556 0.3578 0.0509 0.0187
## 5 0.0403 0.0014 0.0382 0.0000 0.0036 0.4623
## 6 0.0052 0.2489 0.0010 0.0001 0.2076 0.0062
## 7 0.0151 0.1366 0.0000 0.1356 0.3265 0.0034
## 8 0.2580 0.1402 0.0008 0.0082 0.0005 0.0259
## 9 0.0753 0.0463 0.0091 0.0042 0.0159 0.0133
## 10 0.3537 0.2279 0.8096 0.4259 0.3265 0.4585
## 11 0.0025 0.0094 0.0082 0.0073 0.0028 0.0014
##
## ===============================
## Row 9==> GS, proportion 0.929275 >= 0.50
## Row 11==> Wt, proportion 0.989877 >= 0.50
## Row 10==> Position_CLW, proportion 0.522633 >= 0.50
## Row 10==> Position_D, proportion 0.809633 >= 0.50
ols_step_forward_p(model3)
##
## Selection Summary
## ---------------------------------------------------------------------------------------
## Variable Adj.
## Step Entered R-Square R-Square C(p) AIC RMSE
## ---------------------------------------------------------------------------------------
## 1 GS 0.4540 0.4525 20.9978 11365.1352 1801945.3109
## 2 Wt 0.4811 0.4781 4.3585 11348.8823 1759179.4048
## 3 Position_CLW 0.4889 0.4846 0.9425 11345.3998 1748254.9274
## 4 Position_RW 0.4922 0.4865 0.6642 11345.0682 1745046.4442
## 5 Position_CLWRW 0.4938 0.4866 1.5845 11345.9580 1744816.4395
## ---------------------------------------------------------------------------------------
ols_step_backward_p(model3)
##
##
## Elimination Summary
## -------------------------------------------------------------------------------------
## Variable Adj.
## Step Removed R-Square R-Square C(p) AIC RMSE
## -------------------------------------------------------------------------------------
## 1 Position_LW 0.4946 0.4816 9.0013 11353.3568 1753318.2850
## 2 Position_LWRW 0.4946 0.483 7.0365 11351.3931 1750900.2967
## 3 Position_CD 0.4944 0.4844 5.1376 11349.4975 1748658.4451
## 4 Position_D 0.4941 0.4854 3.4020 11347.7700 1746835.5999
## 5 Position_CRW 0.4938 0.4866 1.5845 11345.9580 1744816.4395
## -------------------------------------------------------------------------------------
ols_step_both_p(model3)
##
## Stepwise Selection Summary
## -------------------------------------------------------------------------------------------------
## Added/ Adj.
## Step Variable Removed R-Square R-Square C(p) AIC RMSE
## -------------------------------------------------------------------------------------------------
## 1 GS addition 0.454 0.452 20.9980 11365.1352 1801945.3109
## 2 Wt addition 0.481 0.478 4.3590 11348.8823 1759179.4048
## 3 Position_CLW addition 0.489 0.485 0.9430 11345.3998 1748254.9274
## -------------------------------------------------------------------------------------------------
model4 <- lm(Salary ~ GS + Wt + iHDf + GP + PM, data = NHL)
model4
##
## Call:
## lm(formula = Salary ~ GS + Wt + iHDf + GP + PM, data = NHL)
##
## Coefficients:
## (Intercept) GS Wt iHDf GP PM
## -4287614 85185 25692 2733 -7517 -10305
standard_error4 <- sqrt(deviance(model4)/df.residual(model4))
standard_error4
## [1] 1756011
2*standard_error4
## [1] 3512022
plot(fitted(model4),resid(model4))
abline(h=2*standard_error4, col = "blue")
abline(h=-2*standard_error4, col = "blue")
abline(h=3*standard_error4, col = "red")
abline(h=-3*standard_error4, col = "red")
res_pot_outliers4 <- NHL %>% filter(2*standard_error4 <= abs(resid(model4)) & abs(resid(model4)) < 3*standard_error2)
print(res_pot_outliers4)
## # A tibble: 15 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 925000 96-10-… Nort… MA USA USA 74 196 2015 1 2 R
## 2 832500 95-04-… Lond… ON CAN CAN 72 223 2013 1 9 L
## 3 9000000 87-10-… Madi… WI USA USA 72 202 2006 1 5 R
## 4 7250000 87-04-… Mont… QC CAN CAN 72 201 2005 3 62 R
## 5 925000 97-07-… Gros… MI USA USA 74 218 2015 1 8 L
## 6 7500000 85-04-… Edmo… AB CAN CAN 75 219 2003 1 9 L
## 7 5600000 83-09-… Edmo… AB CAN CAN 76 221 2002 1 3 L
## 8 6000000 83-03-… Kitc… ON CAN CAN 72 202 2002 8 241 R
## 9 9000000 85-01-… Madi… WI USA USA 74 206 2003 1 7 L
## 10 925000 93-05-… St. … AB CAN CAN 78 226 2012 3 86 R
## 11 925000 97-12-… Scot… AZ USA USA 74 202 2016 1 6 L
## 12 9000000 84-07-… Minn… MN USA USA 71 196 2003 1 17 L
## 13 832500 95-03-… Ste-… QC CAN CAN 71 188 2013 1 3 L
## 14 8000000 84-06-… Bram… ON CAN CAN 76 212 2002 1 1 L
## 15 8000000 88-04-… St. … MN USA USA 72 218 2006 1 7 R
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, iCF...42 <dbl>,
## # iFF <dbl>, iSF...44 <dbl>, iSF...45 <dbl>, iSF...46 <dbl>, ixG <dbl>, …
res_outliers4 <- NHL %>% filter(abs(resid(model4)) >= 3*standard_error4)
print(res_outliers4)
## # A tibble: 6 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 13800000 88-04-… Winn… MB CAN CAN 74 201 2006 1 3 L
## 2 13800000 88-11-… Buff… NY USA USA 71 177 2007 1 1 L
## 3 11000000 89-05-… Toro… ON CAN CAN 72 210 2007 2 43 R
## 4 12000000 85-08-… Sica… BC CAN CAN 76 232 2003 2 49 R
## 5 8000000 85-12-… Mapl… BC CAN CAN 75 200 2004 1 4 L
## 6 6500000 85-03-… Roch… NY USA USA 70 187 2004 4 127 R
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, iCF...42 <dbl>,
## # iFF <dbl>, iSF...44 <dbl>, iSF...45 <dbl>, iSF...46 <dbl>, ixG <dbl>, …
h4 <- 2*(5+1)/359
h4
## [1] 0.03342618
leverage4 <- hatvalues(model4)
sort(round(leverage4,4))
## 197 335 22 58 342 97 264 243 87 24 353
## 0.0040 0.0040 0.0041 0.0050 0.0050 0.0052 0.0052 0.0053 0.0054 0.0055 0.0055
## 51 253 196 320 156 116 293 183 329 333 71
## 0.0059 0.0059 0.0060 0.0060 0.0062 0.0063 0.0063 0.0067 0.0067 0.0068 0.0069
## 260 285 95 108 319 86 175 134 216 127 207
## 0.0069 0.0069 0.0070 0.0071 0.0071 0.0072 0.0072 0.0073 0.0073 0.0074 0.0074
## 214 304 14 46 73 225 270 174 235 328 347
## 0.0074 0.0074 0.0075 0.0075 0.0075 0.0075 0.0075 0.0076 0.0076 0.0076 0.0076
## 43 208 68 281 161 106 198 247 352 38 194
## 0.0077 0.0077 0.0078 0.0079 0.0080 0.0081 0.0081 0.0081 0.0081 0.0084 0.0085
## 252 314 173 204 49 119 149 180 89 268 336
## 0.0085 0.0085 0.0086 0.0086 0.0087 0.0087 0.0087 0.0088 0.0089 0.0089 0.0089
## 123 133 178 176 7 81 154 249 310 93 85
## 0.0090 0.0090 0.0090 0.0091 0.0093 0.0093 0.0093 0.0093 0.0093 0.0094 0.0096
## 8 50 63 276 21 142 182 226 245 301 261
## 0.0097 0.0097 0.0097 0.0097 0.0098 0.0098 0.0098 0.0098 0.0098 0.0098 0.0099
## 340 18 279 9 280 40 211 236 287 299 29
## 0.0099 0.0100 0.0100 0.0101 0.0101 0.0102 0.0102 0.0102 0.0102 0.0102 0.0103
## 159 223 96 102 332 348 358 15 37 228 290
## 0.0103 0.0104 0.0105 0.0105 0.0105 0.0105 0.0105 0.0106 0.0106 0.0106 0.0106
## 48 227 256 141 213 300 354 31 255 274 53
## 0.0108 0.0108 0.0108 0.0109 0.0109 0.0110 0.0110 0.0111 0.0111 0.0111 0.0112
## 195 338 5 164 305 150 295 78 107 289 325
## 0.0112 0.0112 0.0113 0.0113 0.0113 0.0114 0.0114 0.0115 0.0115 0.0115 0.0115
## 104 201 206 112 117 251 265 139 165 79 330
## 0.0116 0.0117 0.0117 0.0118 0.0118 0.0118 0.0118 0.0119 0.0119 0.0120 0.0120
## 124 155 238 115 331 27 187 189 297 298 20
## 0.0121 0.0121 0.0121 0.0122 0.0122 0.0123 0.0123 0.0123 0.0123 0.0124 0.0125
## 128 72 138 17 277 30 283 296 2 241 263
## 0.0125 0.0126 0.0126 0.0127 0.0127 0.0128 0.0128 0.0128 0.0129 0.0129 0.0129
## 341 32 35 45 184 351 19 217 257 74 83
## 0.0129 0.0131 0.0131 0.0131 0.0132 0.0132 0.0133 0.0133 0.0133 0.0134 0.0134
## 323 345 145 239 118 185 288 26 169 172 234
## 0.0134 0.0134 0.0135 0.0135 0.0136 0.0136 0.0136 0.0137 0.0137 0.0138 0.0139
## 91 80 303 39 64 114 179 203 199 11 65
## 0.0140 0.0141 0.0141 0.0142 0.0142 0.0142 0.0142 0.0142 0.0143 0.0144 0.0145
## 312 343 218 262 359 109 168 191 28 103 181
## 0.0146 0.0146 0.0148 0.0148 0.0149 0.0150 0.0150 0.0150 0.0151 0.0151 0.0151
## 135 1 209 231 147 171 313 101 113 52 61
## 0.0152 0.0153 0.0153 0.0153 0.0154 0.0154 0.0154 0.0155 0.0156 0.0157 0.0157
## 355 84 258 36 99 126 144 75 242 125 306
## 0.0157 0.0158 0.0158 0.0159 0.0159 0.0160 0.0160 0.0161 0.0162 0.0164 0.0164
## 186 110 222 248 16 286 190 307 212 316 54
## 0.0165 0.0166 0.0167 0.0168 0.0169 0.0170 0.0171 0.0172 0.0173 0.0173 0.0175
## 143 278 62 158 309 67 160 57 250 76 44
## 0.0176 0.0176 0.0178 0.0178 0.0178 0.0179 0.0179 0.0182 0.0183 0.0185 0.0186
## 334 94 272 240 12 308 210 47 291 151 327
## 0.0186 0.0187 0.0187 0.0190 0.0192 0.0192 0.0193 0.0195 0.0197 0.0199 0.0199
## 188 56 294 318 356 266 129 200 267 346 42
## 0.0200 0.0201 0.0202 0.0202 0.0202 0.0204 0.0205 0.0206 0.0208 0.0211 0.0212
## 34 337 13 132 146 224 244 326 4 357 177
## 0.0213 0.0215 0.0216 0.0217 0.0219 0.0219 0.0219 0.0220 0.0221 0.0221 0.0222
## 82 202 130 162 350 60 292 311 166 152 111
## 0.0223 0.0223 0.0225 0.0225 0.0225 0.0228 0.0235 0.0235 0.0237 0.0238 0.0241
## 324 157 90 167 237 92 3 33 77 215 230
## 0.0241 0.0242 0.0243 0.0243 0.0243 0.0249 0.0250 0.0254 0.0257 0.0260 0.0266
## 55 6 100 275 220 205 229 120 232 259 273
## 0.0267 0.0271 0.0272 0.0274 0.0277 0.0280 0.0280 0.0281 0.0282 0.0286 0.0291
## 66 344 153 221 193 269 121 321 69 25 254
## 0.0292 0.0292 0.0293 0.0293 0.0294 0.0297 0.0306 0.0307 0.0311 0.0318 0.0324
## 88 140 233 284 41 339 271 282 322 317 136
## 0.0329 0.0351 0.0355 0.0359 0.0363 0.0367 0.0371 0.0375 0.0378 0.0382 0.0383
## 122 349 246 148 163 131 137 170 302 70 23
## 0.0388 0.0390 0.0398 0.0400 0.0403 0.0419 0.0437 0.0439 0.0458 0.0469 0.0492
## 315 105 10 192 98 59 219
## 0.0495 0.0508 0.0512 0.0530 0.0546 0.0595 0.0648
leverage_outliers4 <- NHL %>% filter(leverage4 > h4)
leverage_outliers4
## # A tibble: 28 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 10900000 87-08… Cole… NS CAN CAN 71 200 2005 1 1 L
## 2 2075000 91-12… St. … ON CAN CAN 75 226 2010 1 21 L
## 3 8750000 85-07… Anci… QC CAN CAN 73 195 2003 2 45 R
## 4 5850000 86-04… Anch… AK USA USA 74 218 2004 2 60 L
## 5 1300000 81-06… Sudb… ON CAN CAN 71 181 1999 5 128 L
## 6 5000000 88-05… Hali… NS CAN CAN 69 181 2006 3 71 L
## 7 1300000 89-04… Otta… ON CAN CAN 69 160 2007 6 179 L
## 8 6000000 84-07… Plov… WI USA USA 71 190 2003 7 205 R
## 9 6000000 92-01… Bram… ON CAN CAN 73 200 2010 1 2 R
## 10 3750000 93-07… Pitt… PA USA USA 70 182 2011 3 64 R
## # ℹ 18 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
t4 <- qt(df = 359 - 5 - 2, 0.95)
t4
## [1] 1.649194
jackknife4 <- rstudent(model4)
sort(round(jackknife4, 4))
## 188 277 36 34 291 273 282 96 193 153
## -2.6253 -2.3645 -2.2988 -2.2731 -2.2010 -2.0879 -1.9679 -1.9582 -1.8552 -1.7966
## 166 261 98 343 254 212 354 64 12 205
## -1.6867 -1.6572 -1.6516 -1.5572 -1.5013 -1.4655 -1.4107 -1.4104 -1.3793 -1.3678
## 77 355 5 342 13 167 317 105 141 312
## -1.3605 -1.3524 -1.3311 -1.3147 -1.3030 -1.3029 -1.2703 -1.2445 -1.2374 -1.2011
## 230 136 72 79 69 339 335 53 178 255
## -1.1757 -1.1747 -1.1710 -1.1449 -1.1143 -1.0741 -1.0036 -1.0012 -0.9938 -0.9821
## 118 359 112 51 108 172 198 323 351 256
## -0.9810 -0.9769 -0.9767 -0.9760 -0.9304 -0.9126 -0.9004 -0.8910 -0.8734 -0.8707
## 245 42 151 117 80 154 327 232 242 226
## -0.8557 -0.8531 -0.8319 -0.8262 -0.8235 -0.8014 -0.7888 -0.7806 -0.7805 -0.7781
## 83 303 260 329 258 162 290 90 60 68
## -0.7533 -0.7436 -0.7149 -0.7045 -0.7036 -0.6925 -0.6859 -0.6659 -0.6656 -0.6509
## 4 92 43 270 349 310 220 344 249 25
## -0.6495 -0.6383 -0.6160 -0.6053 -0.5986 -0.5977 -0.5899 -0.5835 -0.5803 -0.5788
## 346 302 353 210 326 33 221 294 63 211
## -0.5788 -0.5728 -0.5686 -0.5607 -0.5594 -0.5573 -0.5519 -0.5501 -0.5486 -0.5478
## 6 301 299 131 239 275 61 330 38 81
## -0.5236 -0.5201 -0.5059 -0.4999 -0.4963 -0.4922 -0.4910 -0.4878 -0.4837 -0.4810
## 73 143 321 75 87 110 223 233 170 106
## -0.4765 -0.4688 -0.4650 -0.4494 -0.4452 -0.4452 -0.4446 -0.4386 -0.4366 -0.4361
## 280 213 307 197 94 337 194 128 58 78
## -0.4279 -0.4177 -0.4079 -0.4077 -0.4014 -0.3933 -0.3924 -0.3891 -0.3828 -0.3799
## 333 243 164 95 276 278 126 130 168 219
## -0.3643 -0.3605 -0.3496 -0.3440 -0.3374 -0.3357 -0.3225 -0.3174 -0.3158 -0.3141
## 76 150 196 334 3 127 132 2 352 285
## -0.3131 -0.3043 -0.3040 -0.2984 -0.2961 -0.2946 -0.2938 -0.2836 -0.2814 -0.2811
## 345 216 201 322 28 179 123 133 62 314
## -0.2790 -0.2715 -0.2695 -0.2652 -0.2570 -0.2568 -0.2457 -0.2405 -0.2382 -0.2303
## 169 247 122 234 189 336 298 8 246 251
## -0.2267 -0.2188 -0.2166 -0.2156 -0.2154 -0.2133 -0.2126 -0.1986 -0.1932 -0.1926
## 85 17 289 46 295 50 304 324 37 348
## -0.1853 -0.1682 -0.1675 -0.1669 -0.1666 -0.1623 -0.1540 -0.1450 -0.1385 -0.1332
## 292 29 308 19 182 257 207 121 340 18
## -0.1302 -0.1298 -0.1298 -0.1287 -0.1268 -0.1239 -0.1238 -0.1215 -0.1214 -0.1169
## 16 111 206 274 88 236 227 316 296 305
## -0.1156 -0.1118 -0.1114 -0.1097 -0.1090 -0.1027 -0.1016 -0.0949 -0.0925 -0.0923
## 101 338 158 135 263 49 71 113 86 93
## -0.0904 -0.0869 -0.0789 -0.0688 -0.0678 -0.0655 -0.0512 -0.0454 -0.0443 -0.0414
## 7 311 328 27 175 84 103 67 134 32
## -0.0392 -0.0383 -0.0383 -0.0293 -0.0291 -0.0285 -0.0231 -0.0209 -0.0196 -0.0193
## 287 91 82 250 195 202 116 149 40 331
## -0.0187 -0.0157 -0.0094 0.0006 0.0024 0.0068 0.0109 0.0213 0.0279 0.0351
## 183 347 56 159 208 148 142 191 114 21
## 0.0429 0.0471 0.0511 0.0564 0.0584 0.0693 0.0740 0.0803 0.0805 0.0821
## 138 119 115 15 54 225 57 74 144 173
## 0.0824 0.0827 0.0842 0.0859 0.0874 0.0875 0.0932 0.0949 0.1013 0.1028
## 199 181 174 104 11 23 89 155 30 39
## 0.1052 0.1095 0.1135 0.1337 0.1400 0.1400 0.1430 0.1435 0.1541 0.1582
## 26 288 203 145 265 129 177 70 48 204
## 0.1760 0.1900 0.1991 0.2000 0.2027 0.2039 0.2139 0.2230 0.2238 0.2466
## 97 224 35 267 100 52 306 1 65 152
## 0.2590 0.2632 0.2768 0.2852 0.2887 0.2967 0.2987 0.3003 0.3023 0.3133
## 357 66 45 146 313 120 209 252 184 222
## 0.3248 0.3440 0.3543 0.3544 0.3707 0.3713 0.4033 0.4165 0.4283 0.4478
## 156 235 124 341 283 107 214 253 297 248
## 0.4830 0.5103 0.5306 0.5894 0.5959 0.6400 0.6464 0.6550 0.6621 0.6809
## 44 192 262 190 20 318 160 272 55 41
## 0.6942 0.7006 0.7079 0.7231 0.7305 0.7437 0.7531 0.7696 0.7758 0.8076
## 332 356 59 268 102 217 315 286 9 165
## 0.8144 0.8398 0.8427 0.8643 0.8854 0.9058 0.9540 0.9591 0.9725 0.9752
## 147 200 320 269 293 171 31 350 284 241
## 0.9836 1.0004 1.0180 1.0347 1.0911 1.1058 1.1552 1.1636 1.2038 1.2302
## 266 157 125 185 161 14 244 279 140 163
## 1.2435 1.2849 1.3055 1.3271 1.3370 1.3495 1.3609 1.3837 1.3906 1.4293
## 99 180 109 187 237 10 309 240 238 22
## 1.4371 1.4616 1.4683 1.5249 1.5852 1.6171 1.6763 1.6956 1.7183 1.7360
## 215 24 218 231 176 229 139 264 325 319
## 1.7398 1.7879 1.8420 1.9524 2.0585 2.0678 2.1346 2.2200 2.3105 2.3312
## 228 281 271 300 186 358 259 137 47
## 2.6145 2.8114 3.0118 3.0743 3.3727 3.3882 3.7676 4.1387 5.0191
jackknife_outliers4 <- NHL %>% filter(jackknife4 > t4 | jackknife4 < -t4)
jackknife_outliers4
## # A tibble: 36 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 5000000 87-01… St. … MB CAN CAN 72 196 2005 5 132 L
## 2 7000000 85-12… Queb… QC CAN USA 72 202 2005 2 44 L
## 3 925000 96-10… Nort… MA USA USA 74 196 2015 1 2 R
## 4 832500 95-04… Lond… ON CAN CAN 72 223 2013 1 9 L
## 5 13800000 88-04… Winn… MB CAN CAN 74 201 2006 1 3 L
## 6 875000 93-02… Vict… QC CAN CAN 73 193 2011 1 26 L
## 7 5000000 88-05… Hali… NS CAN CAN 69 181 2006 3 71 L
## 8 13800000 88-11… Buff… NY USA USA 71 177 2007 1 1 L
## 9 9000000 87-10… Madi… WI USA USA 72 202 2006 1 5 R
## 10 742500 94-05… Denv… CO USA USA 74 205 2012 4 120 L
## # ℹ 26 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
cookCV4 <- 4/359
cookCV4
## [1] 0.01114206
cook4 <- cooks.distance(model4)
sort(round(cook4, 4))
## 7 11 15 16 18 19 21 27 29 32 37
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 40 46 49 50 54 56 57 67 71 74 82
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 84 86 89 91 93 101 103 104 113 114 115
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 116 119 134 135 138 142 144 148 149 155 158
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 159 173 174 175 181 182 183 191 195 199 202
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 206 207 208 225 227 236 250 257 263 274 287
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 296 304 305 311 316 328 331 338 340 347 348
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 8 17 26 30 39 48 58 85 88 95 97
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 111 121 123 127 129 133 145 169 189 196 197
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 201 203 204 216 234 243 247 251 265 285 288
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 289 292 295 298 308 314 324 336 352 1 2
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002
## 23 28 35 52 62 65 87 150 156 164 177
## 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
## 179 194 252 276 306 333 345 38 45 73 76
## 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0003 0.0003 0.0003 0.0003
## 78 106 122 126 128 132 168 213 223 224 235
## 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
## 246 267 278 280 334 353 3 70 81 100 130
## 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004
## 152 184 209 253 299 301 313 357 43 63 94
## 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005
## 146 211 214 249 270 307 322 330 61 66 68
## 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006
## 75 110 124 222 239 260 310 329 337 120 143
## 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007 0.0007
## 335 107 283 290 341 51 297 108 154 210 226
## 0.0007 0.0008 0.0008 0.0008 0.0008 0.0009 0.0009 0.0010 0.0010 0.0010 0.0010
## 294 320 20 198 219 268 275 321 233 245 326
## 0.0010 0.0010 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0012 0.0012 0.0012
## 332 346 6 83 248 258 262 293 303 33 102
## 0.0012 0.0012 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 0.0014 0.0014
## 117 256 342 44 170 178 190 221 4 9 80
## 0.0014 0.0014 0.0014 0.0015 0.0015 0.0015 0.0015 0.0015 0.0016 0.0016 0.0016
## 60 92 160 220 242 344 351 25 90 131 162
## 0.0017 0.0017 0.0017 0.0017 0.0017 0.0017 0.0017 0.0018 0.0018 0.0018 0.0018
## 217 255 323 53 112 165 172 272 318 22 327
## 0.0018 0.0018 0.0018 0.0019 0.0019 0.0019 0.0019 0.0019 0.0019 0.0020 0.0021
## 118 14 151 161 349 356 359 31 147 42 79
## 0.0022 0.0023 0.0023 0.0024 0.0024 0.0024 0.0024 0.0025 0.0025 0.0026 0.0026
## 302 286 55 141 24 72 232 180 171 279 241
## 0.0026 0.0027 0.0028 0.0028 0.0029 0.0029 0.0030 0.0031 0.0032 0.0032 0.0033
## 5 200 312 354 41 185 264 192 261 125 64
## 0.0034 0.0035 0.0036 0.0037 0.0041 0.0041 0.0042 0.0046 0.0046 0.0047 0.0048
## 187 355 350 266 99 109 269 343 238 12 13
## 0.0048 0.0049 0.0052 0.0053 0.0055 0.0055 0.0055 0.0059 0.0060 0.0062 0.0062
## 212 230 176 319 69 96 157 244 167 339 59
## 0.0063 0.0063 0.0064 0.0064 0.0066 0.0067 0.0068 0.0069 0.0070 0.0073 0.0075
## 315 77 218 309 139 205 284 136 240 231 281
## 0.0079 0.0081 0.0084 0.0084 0.0090 0.0090 0.0090 0.0092 0.0092 0.0098 0.0102
## 325 237 317 166 140 277 228 254 215 105 36
## 0.0102 0.0104 0.0107 0.0115 0.0117 0.0118 0.0120 0.0125 0.0134 0.0138 0.0141
## 163 291 153 300 193 34 358 229 273 188 10
## 0.0143 0.0160 0.0162 0.0171 0.0173 0.0185 0.0197 0.0203 0.0216 0.0231 0.0234
## 282 98 186 271 259 47 137
## 0.0249 0.0261 0.0308 0.0570 0.0670 0.0782 0.1247
cook_outliers4 <- NHL %>% filter(cook4 > cookCV4)
cook_outliers4
## # A tibble: 26 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 10900000 87-08… Cole… NS CAN CAN 71 200 2005 1 1 L
## 2 925000 96-10… Nort… MA USA USA 74 196 2015 1 2 R
## 3 832500 95-04… Lond… ON CAN CAN 72 223 2013 1 9 L
## 4 13800000 88-04… Winn… MB CAN CAN 74 201 2006 1 3 L
## 5 5000000 88-05… Hali… NS CAN CAN 69 181 2006 3 71 L
## 6 1300000 89-04… Otta… ON CAN CAN 69 160 2007 6 179 L
## 7 13800000 88-11… Buff… NY USA USA 71 177 2007 1 1 L
## 8 8000000 84-05… Minn… MN USA USA 75 221 2003 2 62 R
## 9 742500 94-05… Denv… CO USA USA 74 205 2012 4 120 L
## 10 5500000 80-09… San … CA USA USA 75 219 2000 1 18 L
## # ℹ 16 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
ggplot(NHL, aes(x = fitted(model4), y = jackknife4)) + geom_point()+ geom_hline(yintercept = t4, col = "purple") + geom_hline(yintercept = -t4, col = "purple")
qqnorm(resid(model4))
qqline(resid(model4), col = "red", lwd = 2)
qqPlot(resid(model4))
## [1] 47 137
skewness(jackknife4)
## [1] 1.105766
kurtosis(jackknife4)
## [1] 6.239913
ols_vif_tol(model4)
## Variables Tolerance VIF
## 1 GS 0.3994503 2.503440
## 2 Wt 0.8671789 1.153165
## 3 iHDf 0.7841169 1.275320
## 4 GP 0.4441506 2.251489
## 5 PM 0.8817350 1.134128
eigprop(model4)
##
## Call:
## eigprop(mod = model4)
##
## Eigenvalues CI (Intercept) GS Wt iHDf GP PM
## 1 3.5545 1.0000 0.0004 0.0115 0.0003 0.0011 0.0073 0.0001
## 2 1.2219 1.7056 0.0000 0.0096 0.0000 0.2745 0.0000 0.3532
## 3 0.8338 2.0647 0.0000 0.0001 0.0000 0.4912 0.0000 0.4881
## 4 0.3185 3.3405 0.0030 0.2870 0.0029 0.0521 0.0193 0.1237
## 5 0.0690 7.1774 0.0024 0.6914 0.0022 0.0752 0.9719 0.0286
## 6 0.0024 38.5510 0.9942 0.0004 0.9946 0.1059 0.0015 0.0064
##
## ===============================
## Row 5==> GS, proportion 0.691449 >= 0.50
## Row 6==> Wt, proportion 0.994554 >= 0.50
## Row 5==> GP, proportion 0.971910 >= 0.50
ols_step_forward_p(model4)
##
## Selection Summary
## ---------------------------------------------------------------------------------
## Variable Adj.
## Step Entered R-Square R-Square C(p) AIC RMSE
## ---------------------------------------------------------------------------------
## 1 GS 0.4540 0.4525 20.9212 11365.1352 1801945.3109
## 2 Wt 0.4811 0.4781 4.2858 11348.8823 1759179.4048
## 3 GP 0.4829 0.4786 4.9834 11349.5713 1758441.6609
## 4 iHDf 0.4856 0.4798 5.1791 11349.7471 1756455.3684
## 5 PM 0.4873 0.4800 6.0000 11350.5500 1756011.1787
## ---------------------------------------------------------------------------------
ols_step_backward_p(model4)
## [1] "No variables have been removed from the model."
ols_step_both_p(model4)
##
## Stepwise Selection Summary
## ---------------------------------------------------------------------------------------------
## Added/ Adj.
## Step Variable Removed R-Square R-Square C(p) AIC RMSE
## ---------------------------------------------------------------------------------------------
## 1 GS addition 0.454 0.452 20.9210 11365.1352 1801945.3109
## 2 Wt addition 0.481 0.478 4.2860 11348.8823 1759179.4048
## ---------------------------------------------------------------------------------------------
model5 <- lm(Salary ~ GS + Wt, data = NHL)
model5
##
## Call:
## lm(formula = Salary ~ GS + Wt, data = NHL)
##
## Coefficients:
## (Intercept) GS Wt
## -4662102 75325 26773
standard_error5 <- sqrt(deviance(model5)/df.residual(model5))
standard_error5
## [1] 1759179
2*standard_error5
## [1] 3518359
plot(fitted(model5),resid(model5))
abline(h=2*standard_error5, col = "blue")
abline(h=-2*standard_error5, col = "blue")
abline(h=3*standard_error5, col = "red")
abline(h=-3*standard_error5, col = "red")
res_pot_outliers5 <- NHL %>% filter(2*standard_error5 <= abs(resid(model5)) & abs(resid(model5)) < 3*standard_error5)
print(res_pot_outliers5)
## # A tibble: 16 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 925000 96-10-… Nort… MA USA USA 74 196 2015 1 2 R
## 2 832500 95-04-… Lond… ON CAN CAN 72 223 2013 1 9 L
## 3 875000 93-02-… Vict… QC CAN CAN 73 193 2011 1 26 L
## 4 9000000 87-10-… Madi… WI USA USA 72 202 2006 1 5 R
## 5 742500 94-05-… Denv… CO USA USA 74 205 2012 4 120 L
## 6 7250000 87-04-… Mont… QC CAN CAN 72 201 2005 3 62 R
## 7 925000 97-07-… Gros… MI USA USA 74 218 2015 1 8 L
## 8 7500000 85-04-… Edmo… AB CAN CAN 75 219 2003 1 9 L
## 9 6000000 83-03-… Kitc… ON CAN CAN 72 202 2002 8 241 R
## 10 9000000 85-01-… Madi… WI USA USA 74 206 2003 1 7 L
## 11 925000 93-05-… St. … AB CAN CAN 78 226 2012 3 86 R
## 12 925000 97-12-… Scot… AZ USA USA 74 202 2016 1 6 L
## 13 9000000 84-07-… Minn… MN USA USA 71 196 2003 1 17 L
## 14 832500 95-03-… Ste-… QC CAN CAN 71 188 2013 1 3 L
## 15 8000000 84-06-… Bram… ON CAN CAN 76 212 2002 1 1 L
## 16 8000000 88-04-… St. … MN USA USA 72 218 2006 1 7 R
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, iCF...42 <dbl>,
## # iFF <dbl>, iSF...44 <dbl>, iSF...45 <dbl>, iSF...46 <dbl>, ixG <dbl>, …
res_outliers5 <- NHL %>% filter(abs(resid(model5)) >= 3*standard_error5)
print(res_outliers5)
## # A tibble: 6 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 13800000 88-04-… Winn… MB CAN CAN 74 201 2006 1 3 L
## 2 13800000 88-11-… Buff… NY USA USA 71 177 2007 1 1 L
## 3 11000000 89-05-… Toro… ON CAN CAN 72 210 2007 2 43 R
## 4 12000000 85-08-… Sica… BC CAN CAN 76 232 2003 2 49 R
## 5 8000000 85-12-… Mapl… BC CAN CAN 75 200 2004 1 4 L
## 6 6500000 85-03-… Roch… NY USA USA 70 187 2004 4 127 R
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, iCF...42 <dbl>,
## # iFF <dbl>, iSF...44 <dbl>, iSF...45 <dbl>, iSF...46 <dbl>, ixG <dbl>, …
h5 <- 2*(2+1)/359
h5
## [1] 0.01671309
leverage5 <- hatvalues(model5)
sort(round(leverage5,4))
## 51 151 249 316 83 213 238 264 300 351 215
## 0.0028 0.0028 0.0028 0.0028 0.0029 0.0029 0.0029 0.0029 0.0029 0.0029 0.0030
## 335 347 43 73 94 232 254 303 344 226 252
## 0.0030 0.0030 0.0031 0.0031 0.0031 0.0031 0.0031 0.0031 0.0031 0.0032 0.0032
## 185 241 279 294 312 22 197 260 293 5 20
## 0.0033 0.0033 0.0033 0.0033 0.0033 0.0034 0.0034 0.0034 0.0034 0.0035 0.0035
## 107 118 146 164 191 272 79 194 255 270 353
## 0.0035 0.0035 0.0035 0.0035 0.0035 0.0035 0.0036 0.0036 0.0036 0.0036 0.0036
## 214 225 247 290 301 318 230 38 256 237 3
## 0.0037 0.0037 0.0037 0.0037 0.0037 0.0037 0.0038 0.0039 0.0039 0.0040 0.0041
## 63 127 148 174 176 198 58 108 231 245 28
## 0.0041 0.0041 0.0041 0.0041 0.0041 0.0041 0.0042 0.0042 0.0042 0.0042 0.0043
## 40 44 95 169 333 2 205 211 156 250 320
## 0.0043 0.0043 0.0044 0.0044 0.0044 0.0045 0.0045 0.0045 0.0046 0.0046 0.0046
## 342 24 135 196 253 310 180 184 243 78 14
## 0.0046 0.0047 0.0047 0.0047 0.0047 0.0047 0.0048 0.0048 0.0048 0.0049 0.0050
## 69 97 133 167 209 222 285 39 62 207 217
## 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0051 0.0051 0.0051 0.0051
## 227 350 29 68 87 261 314 8 86 116 276
## 0.0051 0.0051 0.0052 0.0052 0.0053 0.0053 0.0053 0.0054 0.0054 0.0054 0.0054
## 336 128 328 7 75 123 295 326 343 201 223
## 0.0054 0.0055 0.0055 0.0056 0.0056 0.0056 0.0056 0.0056 0.0056 0.0057 0.0057
## 263 271 304 319 119 286 37 71 142 166 183
## 0.0057 0.0057 0.0057 0.0057 0.0058 0.0058 0.0059 0.0059 0.0059 0.0059 0.0059
## 208 297 298 329 332 338 340 4 112 251 357
## 0.0059 0.0059 0.0059 0.0059 0.0059 0.0059 0.0059 0.0060 0.0060 0.0060 0.0060
## 93 99 173 189 216 234 274 305 348 16 46
## 0.0061 0.0061 0.0061 0.0061 0.0061 0.0061 0.0061 0.0061 0.0061 0.0062 0.0062
## 67 153 202 236 287 309 150 182 195 18 175
## 0.0062 0.0062 0.0062 0.0062 0.0062 0.0062 0.0063 0.0063 0.0063 0.0064 0.0064
## 228 280 281 17 56 283 330 88 155 163 299
## 0.0064 0.0064 0.0064 0.0065 0.0065 0.0065 0.0065 0.0066 0.0066 0.0066 0.0066
## 49 134 190 257 141 50 81 233 289 352 89
## 0.0067 0.0067 0.0067 0.0067 0.0068 0.0069 0.0069 0.0069 0.0069 0.0069 0.0070
## 103 178 179 331 27 85 15 21 104 124 165
## 0.0070 0.0070 0.0070 0.0070 0.0071 0.0071 0.0072 0.0072 0.0072 0.0072 0.0072
## 168 235 258 268 325 345 66 355 32 55 74
## 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0073 0.0073 0.0074 0.0074 0.0074
## 159 161 229 288 26 48 204 219 53 59 106
## 0.0074 0.0074 0.0074 0.0074 0.0075 0.0075 0.0075 0.0075 0.0076 0.0076 0.0076
## 126 145 149 154 158 138 248 60 239 354 358
## 0.0077 0.0078 0.0079 0.0079 0.0079 0.0080 0.0080 0.0081 0.0081 0.0081 0.0081
## 152 244 315 206 115 147 262 34 113 275 96
## 0.0082 0.0082 0.0082 0.0083 0.0084 0.0084 0.0084 0.0086 0.0086 0.0086 0.0087
## 91 186 143 160 162 199 265 296 19 30 220
## 0.0089 0.0089 0.0090 0.0090 0.0090 0.0090 0.0092 0.0092 0.0093 0.0093 0.0093
## 266 9 64 72 187 11 70 76 35 42 172
## 0.0093 0.0094 0.0094 0.0094 0.0094 0.0095 0.0095 0.0095 0.0096 0.0096 0.0097
## 200 277 313 102 356 181 117 242 269 349 52
## 0.0097 0.0098 0.0098 0.0099 0.0100 0.0101 0.0102 0.0103 0.0103 0.0103 0.0104
## 31 84 61 110 132 334 341 291 139 218 23
## 0.0105 0.0105 0.0106 0.0106 0.0106 0.0106 0.0106 0.0107 0.0110 0.0111 0.0112
## 302 65 308 346 114 317 359 36 306 322 203
## 0.0112 0.0114 0.0114 0.0114 0.0115 0.0115 0.0115 0.0116 0.0117 0.0117 0.0118
## 210 246 100 307 323 47 125 240 80 109 140
## 0.0118 0.0118 0.0119 0.0119 0.0119 0.0120 0.0120 0.0120 0.0124 0.0124 0.0125
## 1 45 212 292 193 278 273 188 171 101 57
## 0.0126 0.0126 0.0126 0.0126 0.0128 0.0129 0.0132 0.0136 0.0137 0.0139 0.0143
## 144 170 337 282 311 12 54 129 267 157 82
## 0.0143 0.0143 0.0146 0.0147 0.0147 0.0148 0.0148 0.0155 0.0157 0.0158 0.0159
## 111 327 25 92 177 130 33 131 224 90 324
## 0.0166 0.0166 0.0167 0.0180 0.0183 0.0184 0.0185 0.0189 0.0190 0.0194 0.0194
## 136 259 122 221 6 321 13 284 121 120 192
## 0.0196 0.0198 0.0202 0.0202 0.0205 0.0210 0.0212 0.0223 0.0225 0.0230 0.0250
## 77 41 339 105 10 137 98
## 0.0255 0.0279 0.0292 0.0294 0.0331 0.0363 0.0424
leverage_outliers5 <- NHL %>% filter(leverage5 > h5)
leverage_outliers5
## # A tibble: 26 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 6000000 90-09… Miss… ON CAN CAN 73 211 2009 1 1 L
## 2 10900000 87-08… Cole… NS CAN CAN 71 200 2005 1 1 L
## 3 667500 96-03… Calg… AB CAN CAN 70 166 2014 3 79 R
## 4 832500 95-04… St-L… QC CAN CAN 77 235 2013 1 21 L
## 5 8750000 85-07… Anci… QC CAN CAN 73 195 2003 2 45 R
## 6 2000000 84-12… Hing… MA USA USA 78 244 2003 1 26 L
## 7 5000000 91-04… Boxf… MA USA USA 75 228 2009 1 19 L
## 8 3800000 89-11… Kitc… ON CAN CAN 72 180 2009 5 130 L
## 9 5000000 88-05… Hali… NS CAN CAN 69 181 2006 3 71 L
## 10 1300000 89-04… Otta… ON CAN CAN 69 160 2007 6 179 L
## # ℹ 16 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
t5 <- qt(df = 359 - 3 - 2, 0.95)
t5
## [1] 1.649169
jackknife5 <- rstudent(model5)
sort(round(jackknife5, 4))
## 188 277 36 273 34 153 291 96 282 261
## -2.6970 -2.3788 -2.2706 -2.2522 -2.0952 -2.0544 -2.0487 -2.0253 -1.7908 -1.6970
## 193 205 343 166 98 354 355 64 230 317
## -1.6766 -1.6464 -1.5622 -1.5491 -1.5459 -1.5089 -1.4317 -1.4176 -1.4132 -1.4112
## 12 77 254 212 13 342 167 141 105 5
## -1.4070 -1.3847 -1.3613 -1.3515 -1.3409 -1.3284 -1.3267 -1.3177 -1.2535 -1.2323
## 72 312 112 151 53 51 255 69 79 198
## -1.1286 -1.1280 -1.1048 -1.0909 -1.0713 -1.0629 -1.0539 -1.0415 -1.0010 -0.9867
## 335 359 118 245 339 42 323 178 108 136
## -0.9707 -0.9578 -0.9523 -0.9426 -0.9420 -0.9413 -0.9282 -0.9215 -0.9137 -0.8998
## 83 80 226 172 117 232 256 351 303 258
## -0.8834 -0.8756 -0.8729 -0.8728 -0.8574 -0.8317 -0.8313 -0.8229 -0.8188 -0.8141
## 154 327 260 329 233 346 294 43 249 25
## -0.7907 -0.7781 -0.7775 -0.7591 -0.7520 -0.7395 -0.7236 -0.7134 -0.7113 -0.6948
## 68 270 321 75 94 242 330 353 61 290
## -0.6940 -0.6518 -0.6497 -0.6458 -0.6440 -0.6437 -0.6310 -0.6260 -0.6253 -0.6231
## 63 210 92 310 213 326 33 4 162 239
## -0.6146 -0.6109 -0.6103 -0.6039 -0.5982 -0.5922 -0.5822 -0.5809 -0.5794 -0.5764
## 349 38 128 90 73 307 344 211 81 221
## -0.5695 -0.5569 -0.5537 -0.5385 -0.5334 -0.5260 -0.5213 -0.5189 -0.4972 -0.4783
## 106 220 299 110 88 333 87 60 302 62
## -0.4668 -0.4631 -0.4610 -0.4537 -0.4395 -0.4384 -0.4367 -0.4338 -0.4162 -0.4080
## 6 246 197 275 78 143 164 223 234 58
## -0.4040 -0.4012 -0.3940 -0.3918 -0.3899 -0.3888 -0.3819 -0.3781 -0.3769 -0.3739
## 243 127 301 28 2 170 194 337 276 17
## -0.3716 -0.3704 -0.3675 -0.3669 -0.3579 -0.3500 -0.3500 -0.3499 -0.3241 -0.3215
## 352 148 280 216 278 247 135 16 95 150
## -0.3166 -0.3101 -0.2999 -0.2966 -0.2878 -0.2877 -0.2607 -0.2582 -0.2572 -0.2481
## 126 196 169 76 123 168 334 324 133 285
## -0.2449 -0.2401 -0.2393 -0.2359 -0.2315 -0.2297 -0.2293 -0.2290 -0.2280 -0.2208
## 85 345 131 158 130 202 201 304 179 314
## -0.2121 -0.2067 -0.2003 -0.1998 -0.1915 -0.1878 -0.1870 -0.1848 -0.1802 -0.1780
## 46 336 101 3 19 227 132 250 189 219
## -0.1761 -0.1716 -0.1695 -0.1593 -0.1562 -0.1531 -0.1501 -0.1412 -0.1366 -0.1364
## 8 91 251 298 50 311 82 289 295 29
## -0.1318 -0.1183 -0.1160 -0.1133 -0.1082 -0.1030 -0.0884 -0.0875 -0.0854 -0.0682
## 18 207 348 84 328 37 191 296 182 236
## -0.0660 -0.0651 -0.0606 -0.0590 -0.0583 -0.0536 -0.0483 -0.0469 -0.0452 -0.0423
## 340 49 116 274 206 111 257 86 122 134
## -0.0381 -0.0363 -0.0358 -0.0314 -0.0288 -0.0276 -0.0276 -0.0226 -0.0166 -0.0146
## 305 142 316 195 322 338 71 113 103 39
## -0.0131 -0.0052 -0.0018 -0.0003 0.0053 0.0079 0.0085 0.0173 0.0182 0.0185
## 175 7 208 263 308 93 56 174 40 287
## 0.0198 0.0201 0.0277 0.0277 0.0310 0.0329 0.0415 0.0415 0.0456 0.0463
## 23 67 121 225 149 54 27 183 89 292
## 0.0478 0.0521 0.0603 0.0617 0.0624 0.0633 0.0636 0.0704 0.0709 0.0769
## 32 347 173 331 144 159 119 114 21 15
## 0.0789 0.0849 0.1061 0.1097 0.1112 0.1216 0.1380 0.1453 0.1582 0.1625
## 203 138 146 115 199 74 181 48 265 57
## 0.1672 0.1721 0.1751 0.1804 0.1866 0.1894 0.2031 0.2130 0.2145 0.2176
## 66 11 155 104 30 222 204 184 97 70
## 0.2192 0.2234 0.2239 0.2297 0.2460 0.2481 0.2567 0.2631 0.2644 0.2672
## 26 288 224 129 145 177 313 100 267 209
## 0.2679 0.2740 0.2849 0.2966 0.3022 0.3195 0.3419 0.3444 0.3683 0.3731
## 35 1 65 45 52 252 306 357 192 120
## 0.3746 0.3790 0.3790 0.3876 0.3881 0.3976 0.3999 0.4235 0.4428 0.4765
## 156 235 152 214 341 297 283 272 190 262
## 0.4803 0.4846 0.5150 0.5240 0.5266 0.5267 0.5473 0.5550 0.5579 0.5649
## 107 20 248 253 124 217 44 356 269 318
## 0.5666 0.5918 0.6289 0.6351 0.6649 0.7164 0.7343 0.7514 0.7675 0.7827
## 268 160 200 102 41 332 320 59 315 55
## 0.7997 0.8222 0.8303 0.8589 0.9268 0.9420 0.9603 0.9744 0.9959 0.9987
## 9 165 147 293 286 157 185 31 266 171
## 1.0169 1.0299 1.0434 1.0504 1.0932 1.0976 1.1062 1.1156 1.1301 1.1598
## 241 163 279 350 244 14 99 161 180 125
## 1.1932 1.1980 1.2485 1.2638 1.2968 1.3223 1.3281 1.3690 1.3732 1.3907
## 284 215 109 237 140 187 238 240 229 22
## 1.4013 1.4838 1.4868 1.5133 1.6129 1.6202 1.6862 1.7345 1.7537 1.7597
## 309 10 24 218 231 176 139 264 319 325
## 1.7804 1.7870 1.8182 1.8203 1.9796 2.1257 2.1410 2.1746 2.3046 2.3268
## 228 271 281 300 358 186 259 137 47
## 2.5769 2.7764 2.8463 3.0856 3.4714 3.5166 3.7355 4.1471 4.9483
jackknife_outliers5 <- NHL %>% filter(jackknife5 > t5 | jackknife5 < -t5)
jackknife_outliers5
## # A tibble: 34 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 10900000 87-08… Cole… NS CAN CAN 71 200 2005 1 1 L
## 2 5000000 87-01… St. … MB CAN CAN 72 196 2005 5 132 L
## 3 7000000 85-12… Queb… QC CAN USA 72 202 2005 2 44 L
## 4 925000 96-10… Nort… MA USA USA 74 196 2015 1 2 R
## 5 832500 95-04… Lond… ON CAN CAN 72 223 2013 1 9 L
## 6 13800000 88-04… Winn… MB CAN CAN 74 201 2006 1 3 L
## 7 875000 93-02… Vict… QC CAN CAN 73 193 2011 1 26 L
## 8 13800000 88-11… Buff… NY USA USA 71 177 2007 1 1 L
## 9 9000000 87-10… Madi… WI USA USA 72 202 2006 1 5 R
## 10 742500 94-05… Denv… CO USA USA 74 205 2012 4 120 L
## # ℹ 24 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
cookCV5 <- 4/359
cookCV5
## [1] 0.01114206
cook5 <- cooks.distance(model5)
sort(round(cook5, 4))
## 3 7 8 18 23 27 29 32 37 39 40
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 49 50 54 56 67 71 82 84 86 89 91
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 93 103 111 113 116 119 121 122 134 142 146
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 149 159 173 174 175 182 183 189 191 195 206
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 207 208 219 225 227 236 250 251 257 263 274
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 287 289 292 295 296 298 305 308 316 322 328
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 331 338 340 347 348 15 16 19 21 46 48
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 66 74 85 95 97 101 104 114 115 123 132
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 133 135 138 144 148 150 155 158 168 169 179
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 181 184 194 196 199 201 202 203 222 247 265
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
## 285 304 311 314 336 345 2 11 17 26 28
## 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 0.0002 0.0002 0.0002
## 30 57 58 70 76 78 126 127 130 145 164
## 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
## 197 204 209 216 243 252 276 280 288 301 334
## 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
## 352 62 73 87 131 213 214 223 234 324 333
## 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
## 344 20 38 88 94 107 156 211 272 275 278
## 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004
## 313 357 35 43 52 60 63 100 129 143 224
## 0.0004 0.0004 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005
## 249 270 290 299 353 1 45 65 81 106 128
## 0.0005 0.0005 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006
## 170 177 235 246 253 294 297 306 310 337 4
## 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007
## 83 110 152 190 220 232 260 267 283 302 303
## 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007
## 326 351 44 68 75 226 318 217 239 256 262
## 0.0007 0.0007 0.0008 0.0008 0.0008 0.0008 0.0008 0.0009 0.0009 0.0009 0.0009
## 330 335 162 341 6 51 118 124 151 248 307
## 0.0009 0.0009 0.0010 0.0010 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011
## 329 349 79 108 245 185 198 233 255 293 61
## 0.0011 0.0011 0.0012 0.0012 0.0012 0.0013 0.0013 0.0013 0.0013 0.0013 0.0014
## 242 312 320 210 268 221 241 258 154 192 279
## 0.0014 0.0014 0.0014 0.0015 0.0015 0.0016 0.0016 0.0016 0.0017 0.0017 0.0017
## 5 69 120 332 90 254 356 160 178 269 33
## 0.0018 0.0018 0.0018 0.0018 0.0019 0.0019 0.0019 0.0020 0.0020 0.0020 0.0021
## 346 215 92 200 286 59 55 102 112 117 172
## 0.0021 0.0022 0.0023 0.0023 0.0023 0.0024 0.0025 0.0025 0.0025 0.0025 0.0025
## 230 165 25 238 315 342 350 14 42 53 167
## 0.0025 0.0026 0.0027 0.0027 0.0027 0.0027 0.0028 0.0029 0.0029 0.0029 0.0030
## 180 237 321 147 80 163 9 327 22 323 359
## 0.0030 0.0030 0.0030 0.0031 0.0032 0.0032 0.0033 0.0034 0.0035 0.0035 0.0035
## 99 72 141 266 205 31 264 343 161 244 166
## 0.0036 0.0040 0.0040 0.0040 0.0041 0.0044 0.0045 0.0045 0.0046 0.0046 0.0047
## 355 261 24 136 231 176 171 354 64 157 309
## 0.0050 0.0051 0.0052 0.0054 0.0055 0.0061 0.0062 0.0062 0.0064 0.0064 0.0066
## 229 212 317 125 41 187 153 339 300 109 12
## 0.0076 0.0077 0.0077 0.0078 0.0082 0.0082 0.0087 0.0089 0.0090 0.0092 0.0099
## 319 140 96 193 240 218 34 325 13 228 271
## 0.0100 0.0109 0.0119 0.0121 0.0121 0.0123 0.0126 0.0129 0.0130 0.0140 0.0144
## 284 291 105 282 77 139 281 277 36 273 358
## 0.0149 0.0151 0.0158 0.0158 0.0167 0.0168 0.0171 0.0184 0.0199 0.0223 0.0319
## 188 98 186 10 259 47 137
## 0.0330 0.0351 0.0360 0.0362 0.0908 0.0933 0.2065
cook_outliers5 <- NHL %>% filter(cook5 > cookCV5)
cook_outliers5
## # A tibble: 27 × 162
## Salary Born City `Pr/St` Cntry Nat Ht Wt DftYr DftRd Ovrl Hand
## <dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 10900000 87-08… Cole… NS CAN CAN 71 200 2005 1 1 L
## 2 667500 96-03… Calg… AB CAN CAN 70 166 2014 3 79 R
## 3 925000 96-10… Nort… MA USA USA 74 196 2015 1 2 R
## 4 832500 95-04… Lond… ON CAN CAN 72 223 2013 1 9 L
## 5 13800000 88-04… Winn… MB CAN CAN 74 201 2006 1 3 L
## 6 2000000 84-12… Hing… MA USA USA 78 244 2003 1 26 L
## 7 875000 93-02… Vict… QC CAN CAN 73 193 2011 1 26 L
## 8 5000000 88-05… Hali… NS CAN CAN 69 181 2006 3 71 L
## 9 1300000 89-04… Otta… ON CAN CAN 69 160 2007 6 179 L
## 10 13800000 88-11… Buff… NY USA USA 71 177 2007 1 1 L
## # ℹ 17 more rows
## # ℹ 150 more variables: `Last Name` <chr>, `First Name` <chr>, Position <chr>,
## # Team <chr>, GP <dbl>, G <dbl>, A <dbl>, A1 <dbl>, A2 <dbl>, PTS <dbl>,
## # PM <dbl>, `E+/-` <dbl>, PIM <dbl>, Shifts <dbl>, TOI <dbl>, TOIX <dbl>,
## # `TOI/GP...29` <dbl>, `TOI/GP...30` <dbl>, `TOI%` <dbl>, `IPP%` <dbl>,
## # `SH%` <dbl>, `SV%` <dbl>, PDO <dbl>, `F/60` <dbl>, `A/60` <dbl>,
## # `Pct%` <dbl>, Diff <dbl>, `Diff/60` <dbl>, iCF...41 <dbl>, …
ggplot(NHL, aes(x = fitted(model5), y = jackknife5)) + geom_point()+ geom_hline(yintercept = t5, col = "purple") + geom_hline(yintercept = -t5, col = "purple")
qqnorm(resid(model5))
qqline(resid(model5), col = "red", lwd = 2)
qqPlot(resid(model5))
## [1] 47 137
skewness(jackknife5)
## [1] 1.07496
kurtosis(jackknife5)
## [1] 6.179353
ols_vif_tol(model5)
## Variables Tolerance VIF
## 1 GS 0.9999249 1.000075
## 2 Wt 0.9999249 1.000075
eigprop(model5)
##
## Call:
## eigprop(mod = model5)
##
## Eigenvalues CI (Intercept) GS Wt
## 1 2.6324 1.0000 0.0007 0.0511 0.0007
## 2 0.3649 2.6860 0.0020 0.9467 0.0021
## 3 0.0027 31.1192 0.9972 0.0022 0.9971
##
## ===============================
## Row 2==> GS, proportion 0.946701 >= 0.50
## Row 3==> Wt, proportion 0.997137 >= 0.50
ols_step_forward_p(model5)
##
## Selection Summary
## ---------------------------------------------------------------------------------
## Variable Adj.
## Step Entered R-Square R-Square C(p) AIC RMSE
## ---------------------------------------------------------------------------------
## 1 GS 0.4540 0.4525 19.5684 11365.1352 1801945.3109
## 2 Wt 0.4811 0.4781 3.0000 11348.8823 1759179.4048
## ---------------------------------------------------------------------------------
ols_step_backward_p(model5)
## [1] "No variables have been removed from the model."
ols_step_both_p(model5)
##
## Stepwise Selection Summary
## ---------------------------------------------------------------------------------------------
## Added/ Adj.
## Step Variable Removed R-Square R-Square C(p) AIC RMSE
## ---------------------------------------------------------------------------------------------
## 1 GS addition 0.454 0.452 19.5680 11365.1352 1801945.3109
## 2 Wt addition 0.481 0.478 3.0000 11348.8823 1759179.4048
## ---------------------------------------------------------------------------------------------